sequence_id stringlengths 7 7 | sequence_name stringlengths 4 573 | sequence listlengths 1 348 | keywords listlengths 1 7 | score int64 1 2.47k | offset_a int64 -14,827 666,262,453B | offset_b int64 0 635M ⌀ | cross_references listlengths 1 128 ⌀ | former_ids listlengths 1 3 ⌀ | author stringlengths 7 231 ⌀ | timestamp timestamp[us]date 1999-12-11 03:00:00 2026-01-19 02:46:49 | filename stringlengths 29 29 | hash stringlengths 32 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A391665 | Decimal expansion of Sum_{k>=1} k * zeta(2*k) * Fibonacci(2*k) / 5^k. | [
"1",
"1",
"4",
"4",
"4",
"6",
"1",
"3",
"5",
"2",
"4",
"3",
"3",
"5",
"4",
"7",
"1",
"6",
"9",
"9",
"3",
"4",
"5",
"3",
"2",
"2",
"0",
"8",
"7",
"3",
"8",
"3",
"3",
"9",
"2",
"4",
"0",
"7",
"4",
"1",
"1",
"8",
"8",
"6",
"5",
"... | [
"nonn",
"cons"
] | 6 | 1 | 3 | [
"A000045",
"A001906",
"A244979",
"A350760",
"A391665",
"A391666"
] | null | Amiram Eldar, Dec 16 2025 | 2025-12-16T03:51:14 | oeisdata/seq/A391/A391665.seq | 74dbaa75ea5f5cc34d9f3203de387fee |
A391666 | Decimal expansion of Sum_{k>=1} k * zeta(2*k) * Lucas(2*k) / 5^k. | [
"2",
"8",
"3",
"8",
"7",
"0",
"5",
"9",
"3",
"3",
"7",
"6",
"5",
"3",
"6",
"2",
"9",
"9",
"0",
"6",
"3",
"5",
"4",
"8",
"2",
"3",
"5",
"6",
"4",
"5",
"4",
"4",
"6",
"2",
"7",
"8",
"4",
"6",
"1",
"9",
"9",
"2",
"6",
"4",
"8",
"... | [
"nonn",
"cons"
] | 5 | 1 | 1 | [
"A000032",
"A005248",
"A244979",
"A350760",
"A391665",
"A391666"
] | null | Amiram Eldar, Dec 16 2025 | 2025-12-16T03:51:29 | oeisdata/seq/A391/A391666.seq | 62edfb8f2e526fff681e6cbbf04dbc27 |
A391667 | Numbers j such that the average of the first j+1 partition numbers (beginning with p(0)) is an integer. | [
"0",
"1",
"22",
"134",
"270",
"433",
"1585",
"3257",
"3819",
"12959",
"17208",
"637373"
] | [
"nonn",
"more"
] | 10 | 1 | 3 | [
"A000041",
"A000070",
"A051177",
"A058856",
"A203023",
"A391667"
] | null | Ilya Gutkovskiy, Dec 16 2025 | 2025-12-21T16:41:25 | oeisdata/seq/A391/A391667.seq | 6e9e1161df631de58a1591f76d6cf8cb |
A391668 | Table read by antidiagonals. T(n,k) is the least number coprime to all numbers in [n+1, n+k]. | [
"3",
"5",
"2",
"5",
"5",
"3",
"7",
"7",
"3",
"2",
"7",
"7",
"7",
"7",
"5",
"11",
"11",
"11",
"11",
"5",
"2",
"11",
"11",
"11",
"11",
"5",
"3",
"3",
"11",
"11",
"11",
"11",
"5",
"5",
"5",
"2",
"11",
"11",
"11",
"11",
"11",
"11",
"7",... | [
"nonn",
"tabl"
] | 32 | 1 | 1 | [
"A007918",
"A053669",
"A053670",
"A053671",
"A053672",
"A053673",
"A060264",
"A391668"
] | null | Elijah Beregovsky, Dec 16 2025 | 2025-12-22T13:52:32 | oeisdata/seq/A391/A391668.seq | 901e1f85cefb0dbd8e836740c42d83c4 |
A391669 | Triangle read by rows: T(n,k) is the number of binary strings of length n that contain exactly k runs of 1's of even length, 0 <= k <= floor((n+1)/3). | [
"1",
"2",
"3",
"1",
"6",
"2",
"10",
"6",
"19",
"12",
"1",
"33",
"28",
"3",
"61",
"56",
"11",
"108",
"119",
"28",
"1",
"197",
"236",
"75",
"4",
"352",
"479",
"176",
"17",
"638",
"940",
"417",
"52",
"1",
"1145",
"1859",
"930",
"157",
"5",
"... | [
"nonn",
"tabf"
] | 25 | 0 | 2 | [
"A000079",
"A028495",
"A119473",
"A384497",
"A391669"
] | null | Félix Balado, Dec 16 2025 | 2025-12-26T20:01:41 | oeisdata/seq/A391/A391669.seq | 51c1fddef345d065504afaa90b1ff120 |
A391670 | Numbers of the form h^i + k^j where h,i,j,k are distinct positive integers and max{h,i,j,k} - min{h,i,j,k} = 3. | [
"9",
"10",
"12",
"13",
"17",
"19",
"65",
"66",
"82",
"83",
"89",
"96",
"106",
"113",
"141",
"259",
"633",
"634",
"841",
"1032",
"1033",
"1240",
"1354",
"1421",
"1539",
"1753",
"4221",
"4339",
"7840",
"7857",
"10177",
"15689",
"15706",
"18026",
"181... | [
"nonn"
] | 8 | 1 | 1 | [
"A000169",
"A000272",
"A007778",
"A007830",
"A008788",
"A008789",
"A391670"
] | null | Dwight Boddorf, Dec 16 2025 | 2025-12-21T16:30:18 | oeisdata/seq/A391/A391670.seq | da74b901cafe428bbc0ac382cbc869ea |
A391672 | Decimal expansion of sqrt(2+sqrt(2+sqrt(2))). | [
"1",
"9",
"6",
"1",
"5",
"7",
"0",
"5",
"6",
"0",
"8",
"0",
"6",
"4",
"6",
"0",
"8",
"9",
"8",
"2",
"5",
"2",
"3",
"6",
"4",
"4",
"7",
"2",
"2",
"6",
"8",
"4",
"7",
"8",
"0",
"7",
"3",
"9",
"4",
"7",
"8",
"6",
"7",
"4",
"6",
"... | [
"nonn",
"cons",
"easy"
] | 18 | 1 | 2 | [
"A187360",
"A272535",
"A391672",
"A391673",
"A391674"
] | null | A.H.M. Smeets, Dec 16 2025 | 2025-12-22T17:37:31 | oeisdata/seq/A391/A391672.seq | 1bc378e655beb283ce66d40eea32ebb0 |
A391673 | Decimal expansion of sqrt(2+sqrt(2-sqrt(2))). | [
"1",
"6",
"6",
"2",
"9",
"3",
"9",
"2",
"2",
"4",
"6",
"0",
"5",
"0",
"9",
"0",
"4",
"7",
"4",
"1",
"5",
"7",
"5",
"7",
"6",
"7",
"5",
"5",
"2",
"3",
"5",
"8",
"1",
"1",
"5",
"1",
"3",
"4",
"7",
"7",
"1",
"2",
"1",
"6",
"2",
"... | [
"nonn",
"cons",
"easy"
] | 17 | 1 | 2 | [
"A187360",
"A272535",
"A391672",
"A391673",
"A391674"
] | null | A.H.M. Smeets, Dec 16 2025 | 2025-12-22T17:38:04 | oeisdata/seq/A391/A391673.seq | baa2ae140ffaa1fbe681f2956bf9d29f |
A391674 | Decimal expansion of sqrt(2-sqrt(2-sqrt(2))). | [
"1",
"1",
"1",
"1",
"1",
"4",
"0",
"4",
"6",
"6",
"0",
"3",
"9",
"2",
"0",
"4",
"4",
"4",
"9",
"4",
"8",
"5",
"6",
"6",
"1",
"6",
"2",
"7",
"8",
"9",
"7",
"0",
"6",
"5",
"7",
"4",
"8",
"7",
"4",
"9",
"8",
"7",
"4",
"3",
"8",
"... | [
"nonn",
"cons",
"easy"
] | 12 | 1 | 6 | [
"A187360",
"A272535",
"A391672",
"A391673",
"A391674"
] | null | A.H.M. Smeets, Dec 16 2025 | 2025-12-22T17:38:49 | oeisdata/seq/A391/A391674.seq | c5bf409351503d5391850e1eab720793 |
A391676 | a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(k,n-k)^2. | [
"1",
"6",
"30",
"176",
"984",
"5232",
"27312",
"140160",
"707952",
"3531168",
"17428896",
"85249536",
"413738240",
"1994390016",
"9556560384",
"45550854144",
"216094481664",
"1020830461440",
"4804034860544",
"22529730809856",
"105326409295872",
"490983551209472",
"2282693... | [
"nonn"
] | 12 | 0 | 2 | [
"A375276",
"A390612",
"A391676"
] | null | Seiichi Manyama, Dec 16 2025 | 2025-12-19T17:19:59 | oeisdata/seq/A391/A391676.seq | 35f85e14266820a98d74e70cc6966eb2 |
A391677 | a(n) = Sum_{k=0..n} (k+1) * 2^k * 3^(n-k) * binomial(k,n-k)^2. | [
"1",
"4",
"24",
"176",
"1052",
"6624",
"41632",
"256768",
"1584912",
"9738944",
"59592704",
"363733248",
"2214201280",
"13448074240",
"81518607360",
"493270777856",
"2980106119424",
"17979034113024",
"108329663973376",
"651968407662592",
"3919659639290880",
"235424482832629... | [
"nonn"
] | 12 | 0 | 2 | [
"A108490",
"A391677",
"A391678"
] | null | Seiichi Manyama, Dec 16 2025 | 2025-12-19T12:41:15 | oeisdata/seq/A391/A391677.seq | 819c7de1e46b131e27f58534538cc847 |
A391678 | a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(k+2,2) * binomial(k,n-k)^2. | [
"1",
"6",
"42",
"368",
"2616",
"18672",
"132112",
"906624",
"6151536",
"41243552",
"273427680",
"1797219840",
"11722297600",
"75943488000",
"489123171840",
"3133819805696",
"19984972283136",
"126915902664192",
"802948305023488",
"5062568720879616",
"31819873105102848",
"199... | [
"nonn"
] | 12 | 0 | 2 | [
"A108490",
"A391677",
"A391678"
] | null | Seiichi Manyama, Dec 16 2025 | 2025-12-19T17:19:11 | oeisdata/seq/A391/A391678.seq | abf9461c9eeeae2d8a3b28709ad255e8 |
A391679 | Number of integer compositions of n that (1) have all parts > 1 and (2) are not the first sums of any finite nonnegative sequence. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"5",
"7",
"21",
"32",
"77",
"123",
"262",
"427",
"845",
"1390",
"2621",
"4327",
"7891",
"13038",
"23210",
"38327",
"67010",
"110517",
"190571",
"313820",
"535303",
"880079",
"1488282",
"2442961",
"4... | [
"nonn",
"easy",
"new"
] | 12 | 1 | 11 | [
"A008965",
"A011782",
"A022340",
"A070211",
"A342527",
"A357213",
"A390307",
"A390432",
"A390447",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390747",
"A391235",
"A391620",
"A391621",
"A391622",
"A391623",
"A391628",
"A391641",
"A39... | null | Gus Wiseman, Jan 05 2026 | 2026-01-13T08:14:20 | oeisdata/seq/A391/A391679.seq | c34097182e717b51545519d7962ef118 |
A391680 | Number of integer compositions of n that are not the first sums of any composition. | [
"1",
"1",
"3",
"6",
"13",
"27",
"57",
"116",
"240",
"485",
"988",
"1989",
"4017",
"8065",
"16214",
"32498",
"65175",
"130504",
"261385",
"523103",
"1046993",
"2094696",
"4191024",
"8383545",
"16770456",
"33544041",
"67094993",
"134196481",
"268407098",
"5368... | [
"nonn",
"easy",
"new"
] | 12 | 1 | 3 | [
"A008965",
"A011782",
"A070211",
"A342527",
"A357213",
"A390307",
"A390432",
"A390445",
"A390446",
"A390447",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391235",
"A391627",
"A391628",
"A391629",
"A391641",
"A39... | null | Gus Wiseman, Jan 04 2026 | 2026-01-15T04:50:55 | oeisdata/seq/A391/A391680.seq | 9d8d1edefefbc9c6cf77e5515527e365 |
A391681 | Number of integer compositions of n with all parts > 1 that are not the first sums of any composition. | [
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"5",
"7",
"19",
"30",
"65",
"106",
"207",
"340",
"626",
"1029",
"1825",
"2996",
"5182",
"8490",
"14431",
"23594",
"39608",
"64634",
"107522",
"175171",
"289453",
"470919",
"774243",
"1258217",
"2060818",
"33459... | [
"nonn",
"easy",
"new"
] | 13 | 1 | 9 | [
"A000120",
"A008965",
"A011782",
"A022340",
"A066099",
"A070211",
"A212804",
"A342527",
"A357213",
"A390307",
"A390432",
"A390445",
"A390447",
"A390567",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391235",
"A391620",
"A39... | null | Gus Wiseman, Jan 06 2026 | 2026-01-15T04:51:07 | oeisdata/seq/A391/A391681.seq | 8ab5b9e81bed77dfad3df0e0560ce6a0 |
A391682 | Number of integer compositions of n that are the first sums of more than one nonnegative sequence. | [
"1",
"2",
"4",
"7",
"13",
"22",
"39",
"65",
"112",
"185",
"313",
"514",
"859",
"1405",
"2328",
"3797",
"6253",
"10178",
"16687",
"27121",
"44320",
"71953",
"117297",
"190274",
"309619",
"501941",
"815656",
"1321693",
"2145541",
"3475426",
"5637351",
"912... | [
"nonn",
"easy",
"new"
] | 15 | 1 | 2 | [
"A008965",
"A011782",
"A070211",
"A342527",
"A357213",
"A390432",
"A390448",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391234",
"A391235",
"A391621",
"A391622",
"A391623",
"A391627",
"A391628",
"A391641",
"A39... | null | Gus Wiseman, Jan 08 2026 | 2026-01-12T04:30:09 | oeisdata/seq/A391/A391682.seq | bf7d04e1ef2c74349c6074268304d42e |
A391683 | Number of integer compositions of n that are the first sums of some composition. | [
"0",
"1",
"1",
"2",
"3",
"5",
"7",
"12",
"16",
"27",
"36",
"59",
"79",
"127",
"170",
"270",
"361",
"568",
"759",
"1185",
"1583",
"2456",
"3280",
"5063",
"6760",
"10391",
"13871",
"21247",
"28358",
"43310",
"57797",
"88052",
"117491",
"178617",
"238... | [
"nonn",
"easy",
"new"
] | 19 | 1 | 4 | [
"A000079",
"A000120",
"A001511",
"A008965",
"A011782",
"A029837",
"A029931",
"A066099",
"A070211",
"A070939",
"A342527",
"A357213",
"A389731",
"A390307",
"A390362",
"A390432",
"A390448",
"A390449",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A39... | null | Gus Wiseman, Jan 08 2026 | 2026-01-12T04:29:33 | oeisdata/seq/A391/A391683.seq | 4170a99fb35e284995b09c86b84397be |
A391685 | Array read by ascending antidiagonals: A(n,k) = (2*n + 1)*2^(2*k+1) - 1 with k >= 0. | [
"1",
"5",
"7",
"9",
"23",
"31",
"13",
"39",
"95",
"127",
"17",
"55",
"159",
"383",
"511",
"21",
"71",
"223",
"639",
"1535",
"2047",
"25",
"87",
"287",
"895",
"2559",
"6143",
"8191",
"29",
"103",
"351",
"1151",
"3583",
"10239",
"24575",
"32767",
... | [
"nonn",
"easy",
"tabl"
] | 10 | 0 | 2 | [
"A016813",
"A020989",
"A083420",
"A098713",
"A140529",
"A153465",
"A206372",
"A391685",
"A391686"
] | null | Stefano Spezia, Dec 17 2025 | 2025-12-22T19:28:46 | oeisdata/seq/A391/A391685.seq | 782a85ea19b9a5fdf3762d31971ef046 |
A391686 | Antidiagonal sums of the array A391685. | [
"1",
"12",
"63",
"274",
"1125",
"4536",
"18187",
"72798",
"291249",
"1165060",
"4660311",
"18641322",
"74565373",
"298261584",
"1193046435",
"4772185846",
"19088743497",
"76354974108",
"305419896559",
"1221679586370",
"4886718345621",
"19546873382632",
"78187493530683",
... | [
"nonn",
"easy"
] | 6 | 0 | 2 | [
"A391685",
"A391686"
] | null | Stefano Spezia, Dec 17 2025 | 2025-12-22T14:41:28 | oeisdata/seq/A391/A391686.seq | 92431ea960f2a0dd91f301d2ef626963 |
A391688 | a(n) = Sum_{k=0..n} (k+1) * 2^(n-k) * binomial(k,n-k)^2. | [
"1",
"2",
"7",
"28",
"89",
"310",
"1059",
"3552",
"11973",
"40074",
"133647",
"444708",
"1475441",
"4884574",
"16139387",
"53231976",
"175300509",
"576477618",
"1893341927",
"6211198636",
"20354724809",
"66640367494",
"217984687571",
"712460959984",
"2326855188597",
... | [
"nonn"
] | 14 | 0 | 2 | [
"A390612",
"A391688",
"A391689"
] | null | Seiichi Manyama, Dec 17 2025 | 2025-12-19T08:37:41 | oeisdata/seq/A391/A391688.seq | 340f9ef9c497d658e332810cae1dc410 |
A391689 | a(n) = Sum_{k=0..n} 2^(n-k) * binomial(k+2,2) * binomial(k,n-k)^2. | [
"1",
"3",
"12",
"58",
"219",
"861",
"3318",
"12372",
"45813",
"167319",
"604368",
"2165214",
"7696031",
"27172929",
"95383482",
"333071064",
"1157671257",
"4007027163",
"13817288372",
"47483201346",
"162669098403",
"555690505189",
"1893323165886",
"6435309038364",
"21... | [
"nonn"
] | 13 | 0 | 2 | [
"A391676",
"A391688",
"A391689"
] | null | Seiichi Manyama, Dec 17 2025 | 2025-12-19T08:37:33 | oeisdata/seq/A391/A391689.seq | 56bb0684111a179f25f8e7c46b46692f |
A391690 | Number of congruences of the lattice of alternating sign matrices of size n such that minima of congruence classes are permutations. | [
"1",
"2",
"12",
"216",
"10480",
"1344096",
"465473984"
] | [
"nonn",
"more"
] | 8 | 1 | 2 | [
"A005130",
"A125791",
"A391690",
"A391691"
] | null | Ludovic Schwob, Dec 17 2025 | 2025-12-23T14:10:58 | oeisdata/seq/A391/A391690.seq | 49125bc5daab2035734a8478d74ce239 |
A391691 | Number of congruences of the lattice of alternating sign matrices of size n such that minima and maxima of congruence classes are permutations. | [
"1",
"2",
"9",
"69",
"716",
"8986",
"128065",
"2043636"
] | [
"nonn",
"more"
] | 6 | 1 | 2 | [
"A005130",
"A125791",
"A391690",
"A391691"
] | null | Ludovic Schwob, Dec 17 2025 | 2025-12-23T14:11:16 | oeisdata/seq/A391/A391691.seq | 1f03648e4283487af9b47547c8e500b1 |
A391692 | Number of distinct sets of the form J(P_s)\J(P_t) where s > t are two permutations of size n differing by a transposition and J(M) is the set of join-irreducible elements below M in the lattice of alternating sign matrices. | [
"0",
"1",
"9",
"52",
"260",
"1291",
"6915",
"41814",
"289758",
"2291381",
"20436469",
"203035832",
"2222932248",
"26583044399",
"344675421975",
"4815660285162",
"72118777001154",
"1152405604102329",
"19570137802779369",
"351953247879257452",
"6682192854727098972",
"13356065... | [
"nonn"
] | 9 | 1 | 3 | [
"A001809",
"A034009",
"A391692"
] | null | Ludovic Schwob, Dec 17 2025 | 2025-12-24T09:55:18 | oeisdata/seq/A391/A391692.seq | 97323233438c3a8fdb9541ab6b1b8605 |
A391693 | Number of invertible n X n Hankel matrices with entries in {0,1}. | [
"1",
"4",
"19",
"78",
"359",
"1526",
"6544",
"27595",
"116025",
"480396",
"1973735",
"8049327"
] | [
"nonn",
"more",
"new"
] | 17 | 1 | 2 | null | null | Jeffrey Shallit, Jan 15 2026 | 2026-01-18T15:01:42 | oeisdata/seq/A391/A391693.seq | 18221ace6479b32c27e0816dbb185a2e |
A391696 | Irregular triangular array read by rows: T(n,k) = position of 1st letter of 1st appearance of the k-th word of length n in the lexicographic ordering of all 01-words, as in A076478. | [
"1",
"2",
"3",
"5",
"7",
"9",
"11",
"14",
"17",
"20",
"23",
"26",
"29",
"32",
"35",
"39",
"43",
"47",
"51",
"55",
"59",
"63",
"67",
"71",
"75",
"79",
"83",
"87",
"91",
"95",
"99",
"104",
"109",
"114",
"119",
"124",
"129",
"134",
"139",
"1... | [
"nonn",
"tabf"
] | 15 | 1 | 2 | [
"A076478",
"A088578",
"A391696"
] | null | Clark Kimberling, Dec 17 2025 | 2025-12-23T00:11:22 | oeisdata/seq/A391/A391696.seq | 0303b9dfbbfba4d96a3ccfccbb429ffd |
A391697 | Total number of 213 patterns in all heapable permutations of length n. | [
"0",
"0",
"0",
"1",
"11",
"110",
"1080",
"11047",
"119531",
"1378337",
"16965766",
"222795401",
"3116148625",
"46318941935",
"729946419128"
] | [
"nonn",
"more"
] | 11 | 1 | 5 | [
"A336282",
"A390832",
"A391181",
"A391508",
"A391697"
] | null | Manolopoulos Panagiotis, Dec 17 2025 | 2025-12-22T19:17:21 | oeisdata/seq/A391/A391697.seq | 07cb66845f84a6bc6168154c10b83a4b |
A391698 | Primes expressible as a*b - (a+b) where a and b are composite numbers. | [
"23",
"41",
"59",
"71",
"97",
"101",
"103",
"113",
"131",
"139",
"149",
"151",
"167",
"179",
"181",
"191",
"199",
"223",
"227",
"233",
"239",
"251",
"257",
"263",
"269",
"271",
"281",
"293",
"307",
"311",
"337",
"347",
"349",
"353",
"359",
"373",... | [
"nonn"
] | 16 | 1 | 1 | [
"A061240",
"A391512",
"A391698",
"A391699"
] | null | Robert Israel, Dec 17 2025 | 2025-12-23T00:09:49 | oeisdata/seq/A391/A391698.seq | e560bedb25ccf2819d84e1d828d8c49e |
A391699 | Primes expressible as a*b*c - (a+b+c) where a, b and c are distinct composite numbers. | [
"197",
"337",
"409",
"547",
"571",
"617",
"691",
"727",
"757",
"827",
"887",
"967",
"971",
"977",
"1039",
"1049",
"1117",
"1151",
"1163",
"1223",
"1279",
"1301",
"1303",
"1439",
"1459",
"1583",
"1597",
"1667",
"1693",
"1723",
"1741",
"1753",
"1759",
... | [
"nonn"
] | 17 | 1 | 1 | [
"A391512",
"A391698",
"A391699"
] | null | Robert Israel, Dec 17 2025 | 2025-12-23T00:09:54 | oeisdata/seq/A391/A391699.seq | 0d9aa19d1c8524b690c1da6b51ae70d8 |
A391700 | a(n) = (8*n)!/(n!*(2*n)!*(5*n)!). | [
"1",
"168",
"120120",
"109830336",
"111767455800",
"120796711203168",
"135699814088494656",
"156601962871480526400",
"184345148248880810942520",
"220333212491971075631534400",
"266541722680469446902877305120",
"325611887892680108101481230360320",
"401008119815310928953801784481793600"
] | [
"nonn",
"easy"
] | 24 | 0 | 2 | [
"A234461",
"A235536",
"A364305",
"A391700"
] | null | Karol A. Penson, Dec 17 2025 | 2025-12-27T18:02:38 | oeisdata/seq/A391/A391700.seq | 20408ae070d3cd549d65433b1a8973cb |
A391701 | a(n) = phi(n) * (sigma(n) - tau(n)). | [
"0",
"1",
"4",
"8",
"16",
"16",
"36",
"44",
"60",
"56",
"100",
"88",
"144",
"120",
"160",
"208",
"256",
"198",
"324",
"288",
"336",
"320",
"484",
"416",
"560",
"456",
"648",
"600",
"784",
"512",
"900",
"912",
"880",
"800",
"1056",
"984",
"1296"... | [
"nonn",
"easy"
] | 19 | 1 | 3 | [
"A000005",
"A000010",
"A000203",
"A002378",
"A024556",
"A056075",
"A062354",
"A062355",
"A065608",
"A391701"
] | null | Aloe Poliszuk, Dec 22 2025 | 2025-12-29T17:37:46 | oeisdata/seq/A391/A391701.seq | 15fdcf2f41fae5bbad7d443d4c435b69 |
A391703 | Numbers m such that there exists a pair of numbers {j,k} with 0 < j < k < m, such that j*m+k and k*m+j have the same squarefree kernel. | [
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"20",
"21",
"22",
"23",
"25",
"27",
"29",
"31",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"43",
"45",
"47",
"49",
"50",
"51",
"53",
"54",
"55",
"56",
"57",
"59",
"61",
"62",
"63",
... | [
"nonn",
"base"
] | 7 | 1 | 1 | [
"A007947",
"A391703",
"A391704"
] | null | Michael De Vlieger, Dec 17 2025 | 2025-12-20T10:38:54 | oeisdata/seq/A391/A391703.seq | 09f2fbc0b6625059ec8fa78020812ab2 |
A391704 | Numbers b such that there exist 3 smaller numbers {i,j,k} that each exceed 0 such that i*b^2 + j*b + k, j*b^2 + k*b + i, and k*b^2 + i*b + j have the same squarefree kernel. | [
"7",
"9",
"10",
"11",
"16",
"22",
"23",
"25",
"29",
"31",
"34",
"36",
"37",
"39",
"43",
"46",
"49",
"51",
"52",
"53",
"55",
"56",
"61",
"64",
"65",
"67",
"70",
"79",
"81",
"85",
"93",
"94",
"95",
"100",
"106",
"107",
"109",
"116",
"121",
... | [
"nonn",
"base"
] | 6 | 1 | 1 | [
"A007947",
"A391703",
"A391704"
] | null | Michael De Vlieger, Dec 17 2025 | 2025-12-20T10:38:49 | oeisdata/seq/A391/A391704.seq | f12868ce19b50d0e9402ed21e96d699a |
A391706 | Decimal expansion of the sum of the reciprocals of the positive even-indexed Pell numbers. | [
"6",
"0",
"0",
"5",
"7",
"7",
"6",
"4",
"2",
"2",
"9",
"9",
"1",
"4",
"4",
"2",
"2",
"3",
"8",
"3",
"5",
"8",
"6",
"2",
"1",
"1",
"4",
"9",
"3",
"8",
"8",
"8",
"6",
"9",
"5",
"1",
"1",
"3",
"7",
"6",
"1",
"1",
"6",
"6",
"2",
"... | [
"nonn",
"cons"
] | 7 | 0 | 1 | [
"A000129",
"A001542",
"A153386",
"A153415",
"A391706",
"A391707",
"A391708",
"A391709"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:55:21 | oeisdata/seq/A391/A391706.seq | fd0faa1b16014a76257433eb0992cd5f |
A391707 | Decimal expansion of the sum of the reciprocals of the odd-indexed Pell numbers. | [
"1",
"2",
"4",
"1",
"6",
"2",
"5",
"4",
"0",
"7",
"5",
"2",
"8",
"3",
"8",
"4",
"3",
"5",
"6",
"9",
"5",
"6",
"5",
"0",
"9",
"4",
"6",
"8",
"3",
"4",
"0",
"9",
"2",
"1",
"4",
"3",
"7",
"8",
"6",
"7",
"6",
"5",
"8",
"5",
"4",
"... | [
"nonn",
"cons"
] | 10 | 1 | 2 | [
"A000129",
"A001653",
"A153387",
"A153416",
"A391706",
"A391707",
"A391708",
"A391709"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:54:45 | oeisdata/seq/A391/A391707.seq | 8e9bdfc963bfa0cbb09b48d5f8764dd5 |
A391708 | Decimal expansion of the sum of the reciprocals of the positive Pell numbers. | [
"1",
"8",
"4",
"2",
"2",
"0",
"3",
"0",
"4",
"9",
"8",
"2",
"7",
"5",
"2",
"8",
"5",
"8",
"0",
"7",
"9",
"2",
"3",
"7",
"1",
"5",
"8",
"3",
"2",
"7",
"9",
"8",
"0",
"8",
"3",
"8",
"9",
"0",
"0",
"5",
"2",
"7",
"0",
"2",
"1",
"... | [
"nonn",
"cons"
] | 7 | 1 | 2 | [
"A000129",
"A079586",
"A093540",
"A391706",
"A391707",
"A391708",
"A391709"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:55:25 | oeisdata/seq/A391/A391708.seq | de0be4fda0c9a20f7a49f028ec13a7a1 |
A391709 | Decimal expansion of the alternating sum of the reciprocals of the positive Pell numbers. | [
"6",
"4",
"1",
"0",
"4",
"7",
"7",
"6",
"5",
"2",
"2",
"9",
"2",
"4",
"0",
"1",
"3",
"3",
"1",
"2",
"0",
"6",
"4",
"7",
"3",
"5",
"3",
"4",
"0",
"2",
"0",
"3",
"4",
"4",
"8",
"6",
"7",
"3",
"0",
"0",
"4",
"6",
"8",
"8",
"7",
"... | [
"nonn",
"cons"
] | 10 | 0 | 1 | [
"A000129",
"A079586",
"A093540",
"A158933",
"A338612",
"A391706",
"A391707",
"A391708",
"A391709"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:54:52 | oeisdata/seq/A391/A391709.seq | 777123a00c7ae4d375bd4cae8b77afd4 |
A391710 | Decimal expansion of Sum_{k>=1} lambda(k)/Fibonacci(2*k), where lambda is the Liouville lambda function (A008836). | [
"5",
"7",
"4",
"8",
"3",
"5",
"7",
"3",
"4",
"2",
"9",
"3",
"3",
"7",
"6",
"2",
"7",
"3",
"3",
"5",
"4",
"0",
"4",
"6",
"4",
"4",
"2",
"7",
"5",
"2",
"7",
"0",
"3",
"7",
"1",
"7",
"8",
"0",
"0",
"0",
"0",
"9",
"6",
"8",
"3",
"... | [
"nonn",
"cons"
] | 6 | 0 | 1 | [
"A000045",
"A001906",
"A008836",
"A132338",
"A391710",
"A391711",
"A391712"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:55:29 | oeisdata/seq/A391/A391710.seq | ff0a5972a0a71307dbe7b4ef37891882 |
A391711 | Fibonacci numbers whose indices are even positive numbers with an odd number of prime factors (counted with multiplicity). | [
"1",
"21",
"144",
"2584",
"6765",
"317811",
"832040",
"2178309",
"267914296",
"701408733",
"4807526976",
"12586269025",
"32951280099",
"27777890035288",
"72723460248141",
"190392490709135",
"498454011879264",
"3416454622906707",
"8944394323791464",
"23416728348467685",
"75401... | [
"nonn",
"easy"
] | 9 | 1 | 2 | [
"A000045",
"A001906",
"A046470",
"A153386",
"A391710",
"A391711",
"A391712"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:55:35 | oeisdata/seq/A391/A391711.seq | cb3778bcf9251a2a31bf02498bb886b2 |
A391712 | Fibonacci numbers whose indices are even positive numbers with an even number of prime factors (counted with multiplicity). | [
"3",
"8",
"55",
"377",
"987",
"17711",
"46368",
"121393",
"5702887",
"14930352",
"39088169",
"102334155",
"1836311903",
"86267571272",
"225851433717",
"591286729879",
"1548008755920",
"4052739537881",
"10610209857723",
"1304969544928657",
"61305790721611591",
"1605006438163... | [
"nonn",
"easy"
] | 8 | 1 | 1 | [
"A000045",
"A001906",
"A063745",
"A153386",
"A391710",
"A391711",
"A391712"
] | null | Amiram Eldar, Dec 18 2025 | 2025-12-18T07:55:17 | oeisdata/seq/A391/A391712.seq | fc07aab5cbd9457579529277903dccfa |
A391714 | Numerators of the convergents given by treating A072193 as continued fraction coefficients after the leading 0. | [
"1",
"3",
"4",
"11",
"48",
"107",
"155",
"572",
"3015",
"6602",
"16219",
"22821",
"39040",
"100901",
"139941",
"660665",
"4103931",
"12972458",
"30048847",
"43021305",
"116091457",
"159112762",
"911655267",
"6540699631",
"20533754160",
"47608207951",
"115750170062... | [
"nonn",
"frac"
] | 6 | 1 | 2 | [
"A072193",
"A086702",
"A391714",
"A391715"
] | null | Jwalin Bhatt, Dec 18 2025 | 2025-12-22T19:37:35 | oeisdata/seq/A391/A391714.seq | 899b5eacb69e66383d1d2abb86d9bba0 |
A391715 | Denominators of the convergents given by treating A072193 as continued fraction coefficients after the leading 0. | [
"2",
"7",
"9",
"25",
"109",
"243",
"352",
"1299",
"6847",
"14993",
"36833",
"51826",
"88659",
"229144",
"317803",
"1500356",
"9319939",
"29460173",
"68240285",
"97700458",
"263641201",
"361341659",
"2070349496",
"14853788131",
"46631713889",
"108117215909",
"26286... | [
"nonn",
"frac"
] | 6 | 1 | 1 | [
"A072193",
"A086702",
"A391714",
"A391715"
] | null | Jwalin Bhatt, Dec 18 2025 | 2025-12-22T19:37:30 | oeisdata/seq/A391/A391715.seq | b75a3e1bf07845bbb2e9145fe5e48508 |
A391717 | a(n) = (n^(n-1) + n^(n+1) - (n+1)^(n-1) - (n-1)^(n+1))/2. | [
"3",
"29",
"360",
"5429",
"96390",
"1970345",
"45589152",
"1178044649",
"33630496350",
"1051224218549",
"35710670605896",
"1310031046948805",
"51614861124308118",
"2173795174945491089",
"97456139148378248832",
"4633969814988576197009",
"232934217186070122928254",
"12341860295723895... | [
"nonn",
"easy",
"changed"
] | 11 | 2 | 1 | [
"A000312",
"A051489",
"A062023",
"A062024",
"A391414",
"A391717"
] | null | Hugo Pfoertner, Dec 18 2025 | 2026-01-07T13:45:20 | oeisdata/seq/A391/A391717.seq | 01bab944aa4e4edfd16cd2bf84e289c3 |
A391718 | X-coordinates of the lower envelope of A022462. | [
"1",
"2",
"4",
"5",
"6",
"7",
"11",
"15",
"23",
"29",
"46",
"61",
"66",
"67",
"71",
"72",
"79",
"91",
"99",
"100",
"101",
"114",
"124",
"125",
"126",
"127",
"137",
"138",
"145",
"146",
"153",
"154",
"156",
"157",
"161",
"162",
"167",
"179",
... | [
"nonn"
] | 9 | 1 | 2 | [
"A022462",
"A388658",
"A391718",
"A391719"
] | null | Hugo Pfoertner, Dec 18 2025 | 2025-12-19T12:40:18 | oeisdata/seq/A391/A391718.seq | 96090fa20c704f880400f1e411f21093 |
A391719 | Y-coordinates of the lower envelope of A022462. | [
"1",
"1",
"3",
"5",
"9",
"11",
"13",
"17",
"41",
"57",
"67",
"153",
"247",
"277",
"311",
"319",
"329",
"383",
"433",
"487",
"497",
"511",
"611",
"621",
"629",
"639",
"647",
"677",
"699",
"797",
"807",
"827",
"839",
"849",
"869",
"911",
"925",
... | [
"nonn"
] | 8 | 1 | 3 | [
"A022462",
"A391718",
"A391719"
] | null | Hugo Pfoertner, Dec 18 2025 | 2025-12-19T12:40:22 | oeisdata/seq/A391/A391719.seq | 120404dd151f4b7f2a335b986def853f |
A391721 | Restricted size Ramsey numbers r*(P_3, C_n). | [
"8",
"6",
"9",
"9",
"13",
"15",
"17",
"18",
"20",
"22"
] | [
"nonn",
"hard",
"more"
] | 19 | 3 | 1 | null | null | Elijah Beregovsky, Dec 18 2025 | 2025-12-29T16:35:40 | oeisdata/seq/A391/A391721.seq | df95f8f6959e1797cb351db8ed2ebdd2 |
A391722 | Weakly primes (A050249) that are also non-insertable primes (A125001). | [
"34101693667",
"40144044691",
"45031673353",
"58058453543",
"89797181359",
"95815971907",
"106071536707",
"171199263119",
"181504380313"
] | [
"base",
"nonn",
"more",
"hard"
] | 15 | 1 | 1 | [
"A050249",
"A125001",
"A391722"
] | null | Emmanuel Vantieghem, Dec 18 2025 | 2026-01-01T17:25:34 | oeisdata/seq/A391/A391722.seq | 3595c92f6fb2fd3c414d950877396ebf |
A391723 | a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k+6,6) * binomial(2*k,2*(n-3*k)). | [
"1",
"0",
"0",
"14",
"42",
"0",
"112",
"2016",
"1008",
"672",
"30240",
"90720",
"21504",
"282240",
"2116800",
"2554944",
"2268000",
"27941760",
"83884416",
"65596608",
"267043392",
"1475544576",
"2431021824",
"2927232000",
"17853158400",
"53704594944",
"6602025830... | [
"nonn"
] | 16 | 0 | 4 | [
"A391723",
"A391724"
] | null | Seiichi Manyama, Dec 18 2025 | 2025-12-21T05:40:04 | oeisdata/seq/A391/A391723.seq | 294f31906a28960d3bbd2c14d92ea787 |
A391724 | a(n) = Sum_{k=0..floor(n/4)} 2^k * 3^(n-3*k) * binomial(n-3*k+6,6) * binomial(2*(n-3*k),2*k). | [
"1",
"21",
"252",
"2268",
"17052",
"115290",
"741636",
"4705452",
"29807631",
"187564167",
"1160653536",
"7015318632",
"41344513938",
"237976030404",
"1341887545224",
"7435262750328",
"40583278223901",
"218600645068953",
"1163518783578900",
"6125571713285892",
"31925464081249... | [
"nonn"
] | 16 | 0 | 2 | [
"A391723",
"A391724"
] | null | Seiichi Manyama, Dec 18 2025 | 2025-12-21T05:40:01 | oeisdata/seq/A391/A391724.seq | 384c4c51d5eacc3fefd8749b930ef355 |
A391725 | Square array read by descending antidiagonals: A(n, k) is the k-th odd number i that satisfies i*n = A048720(i,m) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"1",
"5",
"3",
"1",
"7",
"5",
"3",
"1",
"9",
"7",
"5",
"3",
"1",
"11",
"9",
"7",
"5",
"3",
"1",
"13",
"11",
"9",
"7",
"7",
"3",
"1",
"15",
"13",
"15",
"9",
"9",
"5",
"7",
"1",
"17",
"15",
"17",
"11",
"15",
"7",
"9",
"3",... | [
"nonn",
"tabl"
] | 24 | 1 | 2 | [
"A000012",
"A005408",
"A048720",
"A391570",
"A391582",
"A391584",
"A391725",
"A391726",
"A391735",
"A391741",
"A391743",
"A391745",
"A391847",
"A391849",
"A391851",
"A391853",
"A391855",
"A391857",
"A391859",
"A391861",
"A391925"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-23T15:27:35 | oeisdata/seq/A391/A391725.seq | 44ad189f78a8d2eb1b0e7762b7136ccf |
A391726 | Square array read by descending antidiagonals: find the k-th odd number i that satisfies i*n = A048720(i,m) for some m, then A(n, k) = m. Here A048720 is carryless base-2 multiplication. | [
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"7",
"4",
"1",
"2",
"3",
"4",
"5",
"1",
"2",
"7",
"4",
"5",
"6",
"1",
"2",
"3",
"4",
"13",
"14",
"7",
"1",
"2",
"7",
"4",
"5",
"6",
"11",
"8",
"1",
"2",
"3",
"4",
"13",
"14",
"7",
"8",
"9"... | [
"nonn",
"base",
"tabl"
] | 19 | 1 | 3 | [
"A000012",
"A005408",
"A048720",
"A280500",
"A391571",
"A391583",
"A391725",
"A391726",
"A391736"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-18T20:23:42 | oeisdata/seq/A391/A391726.seq | 7d37dbe527ddbad7f96b8bebc5171ad3 |
A391727 | Numbers k such that A115873(k) is not a binary palindrome (in A006995). | [
"203",
"333",
"405",
"406",
"471",
"666",
"681",
"809",
"810",
"812",
"923",
"939",
"942",
"1209",
"1332",
"1357",
"1362",
"1457",
"1461",
"1465",
"1617",
"1618",
"1620",
"1624",
"1633",
"1659",
"1683",
"1811",
"1846",
"1878",
"1884",
"1899",
"1967",
... | [
"nonn",
"base"
] | 12 | 1 | 1 | [
"A006995",
"A030101",
"A115873",
"A154809",
"A391727",
"A391728",
"A391730"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-21T00:15:41 | oeisdata/seq/A391/A391727.seq | 0e13268d02179a7539234135e14d3368 |
A391728 | Terms of A115873 that are not binary palindromes, in the order of appearance, including duplicates. | [
"83",
"101",
"87",
"83",
"215",
"101",
"879",
"41",
"87",
"83",
"179",
"879",
"215",
"233",
"101",
"109",
"879",
"949",
"959",
"237",
"83",
"41",
"87",
"83",
"1325",
"755",
"959",
"583",
"179",
"879",
"215",
"91",
"815",
"1325",
"3703",
"233",
... | [
"nonn",
"base"
] | 8 | 1 | 1 | [
"A115873",
"A154809",
"A391727",
"A391728",
"A391731"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-21T00:15:11 | oeisdata/seq/A391/A391728.seq | 1f56ffc019e19a1a65bbe711f7862c22 |
A391729 | a(n) = Sum_{k=1..A003817(n)} [A048720(A065621(n),k) == n*k], where [ ] is the Iverson bracket. | [
"1",
"3",
"1",
"7",
"1",
"3",
"1",
"15",
"1",
"3",
"4",
"6",
"3",
"3",
"1",
"31",
"1",
"3",
"4",
"6",
"1",
"8",
"4",
"10",
"1",
"7",
"1",
"6",
"1",
"3",
"1",
"63",
"1",
"3",
"4",
"6",
"5",
"7",
"8",
"10",
"1",
"3",
"12",
"14",
"... | [
"nonn",
"base"
] | 13 | 1 | 2 | [
"A003817",
"A048720",
"A065621",
"A115872",
"A115873",
"A391590",
"A391729"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-20T17:24:35 | oeisdata/seq/A391/A391729.seq | 7458cb74097ef3714ddbd8607e259815 |
A391730 | Numbers k such that A115873(k) is not of the form 2^e - 1. | [
"13",
"26",
"49",
"52",
"57",
"61",
"81",
"98",
"104",
"114",
"122",
"123",
"161",
"162",
"169",
"181",
"193",
"196",
"203",
"205",
"208",
"211",
"228",
"235",
"241",
"244",
"246",
"251",
"253",
"322",
"324",
"333",
"337",
"338",
"357",
"362",
... | [
"nonn",
"base"
] | 11 | 1 | 1 | [
"A000225",
"A036987",
"A115873",
"A391727",
"A391730",
"A391731",
"A391732"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-21T00:15:47 | oeisdata/seq/A391/A391730.seq | 5a1d01c0c18c60deb1a8039f92e061da |
A391731 | Terms of A115873 that are not of the form 2^e - 1, in the order of appearance, including duplicates. | [
"5",
"5",
"21",
"5",
"9",
"21",
"51",
"21",
"5",
"9",
"21",
"51",
"51",
"51",
"219",
"119",
"85",
"21",
"83",
"5",
"5",
"119",
"9",
"219",
"17",
"21",
"51",
"51",
"85",
"51",
"51",
"101",
"219",
"219",
"231",
"119",
"85",
"21",
"87",
"83"... | [
"nonn",
"base",
"look"
] | 12 | 1 | 1 | [
"A000225",
"A115873",
"A391728",
"A391730",
"A391731"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-21T00:15:37 | oeisdata/seq/A391/A391731.seq | c1e57a4c52e2c15132c1fd1e287924a8 |
A391732 | Numbers k such that A115873(k) is of the form 2^e - 1. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",... | [
"nonn",
"base"
] | 10 | 1 | 2 | [
"A000225",
"A036987",
"A115873",
"A391590",
"A391730",
"A391732"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-21T10:48:40 | oeisdata/seq/A391/A391732.seq | caf9c33f6ef35f532baa5de6310f8dbe |
A391733 | Numbers in whose binary expansion there is exactly one run of 1-bits with an odd length, while all other run of 1-bits are of an even length (or absent). | [
"1",
"2",
"4",
"7",
"8",
"11",
"13",
"14",
"16",
"19",
"22",
"25",
"26",
"28",
"31",
"32",
"35",
"38",
"44",
"47",
"49",
"50",
"52",
"55",
"56",
"59",
"61",
"62",
"64",
"67",
"70",
"76",
"79",
"88",
"91",
"94",
"97",
"98",
"100",
"103",
... | [
"nonn",
"base",
"easy"
] | 13 | 1 | 2 | [
"A000079",
"A000396",
"A000668",
"A005940",
"A007088",
"A229125",
"A233868",
"A358769",
"A391733"
] | null | Antti Karttunen, Dec 29 2025 | 2025-12-29T17:02:52 | oeisdata/seq/A391/A391733.seq | 8a988113147a34d2ad30795c961f7823 |
A391734 | Right edge of triangle A240673: a(n) = A002110(n-1) * A079276(n). | [
"1",
"4",
"6",
"120",
"210",
"6930",
"450450",
"9189180",
"193993800",
"2677114440",
"116454478140",
"5415133233510",
"51945166943670",
"1521251317636050",
"562558737261811290",
"1229779565176982820",
"130356633908760178920",
"19227603501542126390700",
"4456958491657464897364260"... | [
"nonn"
] | 8 | 1 | 2 | [
"A002110",
"A079276",
"A240673",
"A245458",
"A391734"
] | null | Antti Karttunen, Dec 31 2025 | 2025-12-31T22:20:01 | oeisdata/seq/A391/A391734.seq | 8fc72b5b749e27b637aaa2a1404b0659 |
A391735 | Square array read by descending antidiagonals: A(n, k) is the k-th odd number i such that i divides A048720(n,i), where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"1",
"5",
"3",
"1",
"7",
"5",
"5",
"1",
"9",
"7",
"9",
"3",
"1",
"11",
"9",
"17",
"5",
"3",
"1",
"13",
"11",
"21",
"7",
"9",
"5",
"1",
"15",
"13",
"33",
"9",
"17",
"9",
"3",
"1",
"17",
"15",
"37",
"11",
"19",
"17",
"7",
... | [
"nonn",
"base",
"tabl"
] | 7 | 1 | 2 | [
"A005408",
"A048720",
"A391572",
"A391725",
"A391735",
"A391736"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-18T22:24:24 | oeisdata/seq/A391/A391735.seq | 863261f9b67ade1ce8534c2ac0658c25 |
A391736 | Square array read by descending antidiagonals: A(n, k) is the value of quotient A048720(n,i)/i for the k-th odd number i which divides A048720(n,i), where A048720 is carryless base-2 multiplication. | [
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"3",
"4",
"1",
"2",
"3",
"4",
"5",
"1",
"2",
"3",
"4",
"5",
"6",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"1",
"2",
"3",
"4",
"5",
"6",
"3",
"8",
"1",
"2",
"3",
"4",
"5",
"6",
"3",
"8",
"9",
"... | [
"nonn",
"base",
"tabl"
] | 11 | 1 | 3 | [
"A000012",
"A115861",
"A391573",
"A391726",
"A391735",
"A391736"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-18T22:24:35 | oeisdata/seq/A391/A391736.seq | ce52ed7ea0e237e6814e01a8f1a9449a |
A391737 | Numbers k such that 25*k = A048720(25, k), where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"4",
"5",
"8",
"10",
"16",
"20",
"32",
"33",
"40",
"64",
"65",
"66",
"80",
"128",
"129",
"130",
"132",
"133",
"160",
"161",
"256",
"257",
"258",
"260",
"261",
"264",
"266",
"320",
"321",
"322",
"512",
"513",
"514",
"516",
"517"... | [
"nonn",
"base"
] | 14 | 1 | 3 | [
"A048720",
"A115422",
"A115831",
"A391737",
"A391738",
"A391739",
"A391858"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-22T10:04:16 | oeisdata/seq/A391/A391737.seq | b855f2535e19ef355ac5da29491fe30a |
A391738 | Numbers k such that 25*k = A048720(41, k), where A048720 is carryless base-2 multiplication. | [
"0",
"31",
"62",
"63",
"93",
"95",
"124",
"125",
"126",
"127",
"186",
"190",
"191",
"248",
"250",
"252",
"253",
"254",
"255",
"372",
"380",
"381",
"382",
"383",
"496",
"500",
"504",
"506",
"508",
"509",
"510",
"511",
"744",
"760",
"762",
"764",
... | [
"nonn",
"base"
] | 9 | 1 | 2 | [
"A048720",
"A115872",
"A391737",
"A391738",
"A391739",
"A391858"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-22T12:41:02 | oeisdata/seq/A391/A391738.seq | c6d27972c110f0f38349ccc5513ac99e |
A391739 | Numbers k such that 25*k = A048720(57, k), where A048720 is carryless base-2 multiplication. | [
"0",
"3",
"6",
"7",
"12",
"14",
"24",
"28",
"48",
"51",
"56",
"96",
"102",
"112",
"192",
"204",
"224",
"384",
"387",
"408",
"448",
"768",
"771",
"774",
"775",
"816",
"819",
"896",
"899",
"1536",
"1539",
"1542",
"1543",
"1548",
"1550",
"1632",
"... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A048720",
"A391737",
"A391738",
"A391739",
"A391858"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-22T10:04:21 | oeisdata/seq/A391/A391739.seq | 729fd73bec0eb102f6b8b1ad9cd37a40 |
A391740 | Numbers k such that 5*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"12",
"14",
"15",
"16",
"17",
"18",
"19",
"24",
"25",
"28",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"38",
"48",
"49",
"50",
"51",
"56",
"60",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"70",... | [
"nonn",
"base"
] | 19 | 1 | 3 | [
"A004742",
"A048716",
"A048720",
"A115770",
"A280500",
"A391585",
"A391740",
"A391741",
"A391742",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-29T07:32:59 | oeisdata/seq/A391/A391740.seq | 04b10559192ea4e449d1d6e012207a8e |
A391741 | Odd numbers k such that 5*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"7",
"9",
"15",
"17",
"19",
"25",
"31",
"33",
"35",
"49",
"51",
"63",
"65",
"67",
"73",
"97",
"99",
"127",
"129",
"131",
"137",
"145",
"147",
"153",
"193",
"195",
"201",
"255",
"257",
"259",
"265",
"273",
"275",
"281",
"289",
"291",... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A048720",
"A280500",
"A391584",
"A391725",
"A391740",
"A391741",
"A391743"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T12:22:22 | oeisdata/seq/A391/A391741.seq | 1fd619f01281eafc777f9f7aa96fbfb1 |
A391742 | Numbers k such that 7*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"4",
"7",
"8",
"9",
"14",
"15",
"16",
"17",
"18",
"28",
"30",
"31",
"32",
"33",
"34",
"36",
"56",
"60",
"62",
"63",
"64",
"65",
"66",
"68",
"72",
"73",
"112",
"120",
"124",
"126",
"127",
"128",
"129",
"130",
"132",
"136",
"... | [
"nonn",
"base"
] | 22 | 1 | 3 | [
"A048715",
"A048720",
"A115770",
"A280500",
"A391585",
"A391740",
"A391742",
"A391743",
"A391744",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-29T07:33:03 | oeisdata/seq/A391/A391742.seq | 55489ddc98f791846397f732fe1326ad |
A391743 | Odd numbers k such that 7*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"7",
"9",
"15",
"17",
"31",
"33",
"63",
"65",
"73",
"127",
"129",
"137",
"145",
"255",
"257",
"265",
"273",
"289",
"455",
"511",
"513",
"521",
"529",
"545",
"577",
"585",
"903",
"911",
"967",
"1023",
"1025",
"1033",
"1041",
"1057",
"1089",
... | [
"nonn",
"base"
] | 6 | 1 | 2 | [
"A048720",
"A280500",
"A391584",
"A391725",
"A391741",
"A391742",
"A391743",
"A391745"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T12:22:26 | oeisdata/seq/A391/A391743.seq | 0ca244b7d617707171fe593ae32596a2 |
A391744 | Numbers k such that 9*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"10",
"12",
"14",
"15",
"16",
"17",
"20",
"21",
"24",
"28",
"30",
"31",
"32",
"33",
"34",
"35",
"40",
"42",
"48",
"49",
"56",
"60",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",... | [
"nonn",
"base"
] | 18 | 1 | 3 | [
"A048720",
"A115801",
"A115845",
"A280500",
"A391585",
"A391740",
"A391742",
"A391744",
"A391745",
"A391846",
"A391848",
"A391850",
"A391852",
"A391854",
"A391856",
"A391858",
"A391860",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-29T07:32:36 | oeisdata/seq/A391/A391744.seq | 012d50d6ac8da819aae4b9f1dd04a7ba |
A391745 | Odd numbers k such that 9*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"7",
"15",
"17",
"21",
"31",
"33",
"35",
"49",
"63",
"65",
"67",
"69",
"71",
"81",
"85",
"97",
"99",
"113",
"127",
"129",
"131",
"133",
"135",
"161",
"163",
"193",
"195",
"197",
"199",
"225",
"227",
"255",
"257",
"259",
"261",
... | [
"nonn",
"base"
] | 6 | 1 | 2 | [
"A048720",
"A280500",
"A391584",
"A391725",
"A391741",
"A391743",
"A391744",
"A391745"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T12:22:29 | oeisdata/seq/A391/A391745.seq | e6690c09f9fe13f9c572f0c549d739b8 |
A391746 | Number of terms of A391909 <= n. | [
"1",
"2",
"3",
"3",
"4",
"5",
"6",
"6",
"6",
"6",
"7",
"8",
"9",
"10",
"11",
"11",
"12",
"13",
"14",
"14",
"14",
"14",
"15",
"15",
"15",
"16",
"16",
"17",
"18",
"19",
"20",
"20",
"21",
"21",
"22",
"23",
"24",
"25",
"25",
"25",
"26",
"... | [
"nonn",
"new"
] | 11 | 1 | 2 | [
"A195017",
"A391746",
"A391747",
"A391909"
] | null | Antti Karttunen and Peter Munn, Jan 02 2026 | 2026-01-04T23:27:11 | oeisdata/seq/A391/A391746.seq | 7a6401e636b8f8927827aab365ae4bd1 |
A391747 | a(n) = 1 if -1 <= A195017(n) <= 1, otherwise 0, where A195017(n) = Sum_{k >= 1} c_k*((-1)^(k-1)), when n = Product_{k >= 1} (p_k)^(c_k), with p_k the k-th prime. | [
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"... | [
"nonn",
"easy"
] | 16 | 1 | null | [
"A003961",
"A008578",
"A195017",
"A297845",
"A353370",
"A391747",
"A391909"
] | null | Antti Karttunen and Peter Munn, Dec 23 2025 | 2026-01-01T10:56:22 | oeisdata/seq/A391/A391747.seq | 64709bd02ebf999a6dc21e2f38c8d191 |
A391749 | Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^3. | [
"112",
"736",
"257536",
"2718416",
"4175872",
"4427408",
"8699888",
"17145500"
] | [
"nonn",
"hard",
"more"
] | 6 | 1 | 1 | [
"A000010",
"A000203",
"A001221",
"A001615",
"A390049",
"A391312",
"A391749"
] | null | S. I. Dimitrov, Dec 18 2025 | 2025-12-22T22:50:40 | oeisdata/seq/A391/A391749.seq | 08f3f78b20ac291551c4b29ac3b96206 |
A391750 | Maximum length of an increasing sequence, bounded by n, in which the largest prime divisors of the elements form a decreasing sequence. | [
"1",
"1",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"... | [
"nonn"
] | 21 | 2 | 3 | [
"A000523",
"A391750",
"A391751"
] | null | Elijah Beregovsky, Dec 18 2025 | 2025-12-30T17:42:36 | oeisdata/seq/A391/A391750.seq | 210fde8b0e1983e7ba04646726af56bf |
A391751 | Indices of record high values in A391750. | [
"4",
"8",
"16",
"32",
"48",
"54",
"64",
"108",
"120",
"128",
"192",
"225",
"243",
"256",
"324",
"384",
"432",
"450",
"486",
"512",
"648",
"729",
"800",
"864",
"972",
"1024",
"1125",
"1152",
"1296",
"1400",
"1440",
"1458",
"1728",
"1944"
] | [
"nonn"
] | 9 | 1 | 1 | [
"A391750",
"A391751"
] | null | Elijah Beregovsky, Dec 18 2025 | 2025-12-24T13:07:24 | oeisdata/seq/A391/A391751.seq | aa3ca919440efc03c6a62f0f3a43682f |
A391752 | First nonzero digit in the decimal expansion of 1/Fibonacci(n). | [
"1",
"1",
"5",
"3",
"2",
"1",
"7",
"4",
"2",
"1",
"1",
"6",
"4",
"2",
"1",
"1",
"6",
"3",
"2",
"1",
"9",
"5",
"3",
"2",
"1",
"8",
"5",
"3",
"1",
"1",
"7",
"4",
"2",
"1",
"1",
"6",
"4",
"2",
"1",
"9",
"6",
"3",
"2",
"1",
"8",
"... | [
"nonn",
"base"
] | 29 | 1 | 3 | [
"A000045",
"A052038",
"A353179",
"A391752"
] | null | Geddes Cureton, Dec 18 2025 | 2025-12-28T21:22:25 | oeisdata/seq/A391/A391752.seq | f9da980080ca4cb4e661d48cb9b23e04 |
A391753 | Number of pairs {j,k}, 0 < j < k < n, such that j*n + k and k*n + j are distinct and have the same squarefree kernel. | [
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"4",
"0",
"4",
"0",
"2",
"0",
"2",
"0",
"7",
"2",
"4",
"3",
"3",
"0",
"3",
"0",
"1",
"0",
"20",
"0",
"6",
"0",
"1",
"10",
"5",
"1",
"2",
"3",
"4",
"1",
"20",
"0",
"17",
"0",
"1",
"0",
"3",... | [
"nonn",
"new"
] | 12 | 3 | 9 | [
"A007947",
"A391703",
"A391753"
] | null | Michael De Vlieger, Dec 21 2025 | 2026-01-12T13:30:28 | oeisdata/seq/A391/A391753.seq | 4f50b46be9ce7977bac450eabef91f44 |
A391754 | a(n) = number of solutions involving 3 smaller numbers {i,j,k} that each exceed 0 such that i*n^2 + j*n + k, j*n^2 + k*n + i, and k*n^2 + i*n + j are distinct and have the same squarefree kernel. | [
"0",
"0",
"0",
"0",
"2",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"2",
"2",
"0",
"8",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"3",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"0",
"... | [
"nonn"
] | 6 | 3 | 5 | [
"A007947",
"A391704",
"A391754"
] | null | Michael De Vlieger, Dec 22 2025 | 2026-01-04T17:32:00 | oeisdata/seq/A391/A391754.seq | 3c732af1b8debb9dca005d214cfa3283 |
A391755 | Cubefull numbers with more than 2 distinct prime factors. | [
"27000",
"54000",
"74088",
"81000",
"108000",
"135000",
"148176",
"162000",
"216000",
"222264",
"243000",
"270000",
"287496",
"296352",
"324000",
"343000",
"405000",
"432000",
"444528",
"474552",
"486000",
"518616",
"540000",
"574992",
"592704",
"648000",
"666792"... | [
"nonn",
"easy"
] | 10 | 1 | 1 | [
"A000977",
"A001694",
"A036966",
"A126706",
"A286708",
"A390950",
"A391755"
] | null | Michael De Vlieger, Dec 22 2025 | 2025-12-24T04:10:11 | oeisdata/seq/A391/A391755.seq | e460fdc8fef2fc9d54ea270a5c00e9d7 |
A391756 | Powers k^m, m > 1, of even k that are not perfect powers. | [
"36",
"100",
"144",
"196",
"216",
"324",
"400",
"484",
"576",
"676",
"784",
"900",
"1000",
"1156",
"1296",
"1444",
"1600",
"1728",
"1764",
"1936",
"2116",
"2304",
"2500",
"2704",
"2744",
"2916",
"3136",
"3364",
"3600",
"3844",
"4356",
"4624",
"4900",
... | [
"nonn",
"easy"
] | 9 | 1 | 1 | [
"A000079",
"A001597",
"A001694",
"A007916",
"A075090",
"A126706",
"A131605",
"A216419",
"A286708",
"A390010",
"A390952",
"A390956",
"A391320",
"A391376",
"A391756"
] | null | Michael De Vlieger, Dec 18 2025 | 2025-12-20T10:39:00 | oeisdata/seq/A391/A391756.seq | 9d63370da7fe567464d23b2c9e67c210 |
A391757 | a(n) = Sum_{k=0..floor(n/4)} 2^k * 3^(n-3*k) * binomial(2*(n-3*k),2*k). | [
"1",
"3",
"9",
"27",
"87",
"351",
"1539",
"6723",
"28467",
"117531",
"479763",
"1955907",
"7998075",
"32807835",
"134797203",
"554013027",
"2276268075",
"9348884811",
"38388273219",
"157620118995",
"647198010171",
"2657558176443",
"10912933399635",
"44813051604675",
"... | [
"nonn"
] | 14 | 0 | 2 | [
"A391724",
"A391757",
"A391758"
] | null | Seiichi Manyama, Dec 18 2025 | 2025-12-19T08:37:27 | oeisdata/seq/A391/A391757.seq | 86f036c18eaf02a704791c92b3677bcf |
A391758 | a(n) = Sum_{k=0..floor(n/4)} (n-3*k+1) * 2^k * 3^(n-3*k) * binomial(2*(n-3*k),2*k). | [
"1",
"6",
"27",
"108",
"417",
"1782",
"8343",
"40176",
"190377",
"876906",
"3947211",
"17522244",
"77243517",
"339290046",
"1486173663",
"6490123704",
"28248529761",
"122547210930",
"530018594883",
"2286202048812",
"9838251072261",
"42248728829286",
"181086392267559",
"... | [
"nonn"
] | 13 | 0 | 2 | [
"A391724",
"A391757",
"A391758"
] | null | Seiichi Manyama, Dec 18 2025 | 2025-12-19T08:37:15 | oeisdata/seq/A391/A391758.seq | 798a76aed547f35c7a321cd12a198a2a |
A391759 | Strictly increasing continued fraction that produces its own decimal expansion (no leading zeros). | [
"0",
"3",
"29",
"54",
"78",
"4380",
"7451",
"15728",
"38929",
"67587",
"310354",
"854187",
"6625304",
"28257282",
"33111342",
"170519293",
"541771999",
"881680510",
"1329276141",
"2664558797",
"8987191257",
"9905072333",
"48257149577",
"246581589739",
"1029715907063",... | [
"nonn",
"base",
"cofr"
] | 12 | 0 | 2 | [
"A039662",
"A091694",
"A113307",
"A378147",
"A391759",
"A391760",
"A391761"
] | null | Jason Bard, Dec 19 2025 | 2025-12-27T21:52:49 | oeisdata/seq/A391/A391759.seq | 265bd414c2efa05d20daf0b69ce73f24 |
A391760 | Strictly increasing continued fraction that produces its own decimal expansion (with leading zeros). | [
"0",
"3",
"29",
"54",
"78",
"438",
"746",
"6087",
"17474",
"70993",
"630096",
"757426",
"915084",
"2213281",
"7874124",
"12376990",
"22264783",
"53124321",
"65077061",
"366026222",
"2428195472",
"6724150081",
"8818626101",
"28559951371",
"71554259371",
"155444039156... | [
"nonn",
"base",
"cofr"
] | 12 | 0 | 2 | [
"A039662",
"A091694",
"A113307",
"A378147",
"A391759",
"A391760",
"A391761"
] | null | Jason Bard, Dec 19 2025 | 2026-01-01T15:44:53 | oeisdata/seq/A391/A391760.seq | 1c88b38b5553ad3980813a1d5f4e865a |
A391761 | Continued fraction that converts to its own decimal expansion; the sequence becomes strictly increasing when all zero terms are removed. | [
"0",
"3",
"29",
"54",
"78",
"438",
"0",
"745",
"5640",
"41468",
"70856",
"456305",
"0",
"810004",
"0",
"2384373",
"3438294",
"0",
"31206699",
"76531931",
"408722091",
"849627628",
"4360218434",
"7215407476",
"34641243880",
"52241626833",
"77511901788",
"57857963... | [
"nonn",
"base",
"cofr"
] | 10 | 0 | 2 | [
"A039662",
"A091694",
"A113307",
"A378147",
"A391759",
"A391760",
"A391761"
] | null | Jason Bard, Dec 20 2025 | 2025-12-30T16:51:52 | oeisdata/seq/A391/A391761.seq | d2338af90de09f6f1d01d8751b509667 |
A391763 | Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^4. | [
"2964",
"3008",
"61184",
"2168010",
"16707584",
"16986500",
"43252398",
"147053264",
"4293853184"
] | [
"nonn",
"hard",
"more"
] | 12 | 1 | 1 | [
"A000010",
"A000203",
"A001221",
"A001615",
"A390049",
"A391312",
"A391749",
"A391763"
] | null | S. I. Dimitrov, Dec 19 2025 | 2025-12-27T15:59:19 | oeisdata/seq/A391/A391763.seq | 0bc48e42009d942e67532360693cdfb1 |
A391765 | a(n) is smallest k such that prime(k) - 1 == 0 (mod n). | [
"1",
"2",
"4",
"3",
"5",
"4",
"10",
"7",
"8",
"5",
"9",
"6",
"16",
"10",
"11",
"7",
"27",
"8",
"43",
"13",
"14",
"9",
"15",
"21",
"26",
"16",
"29",
"10",
"17",
"11",
"64",
"25",
"19",
"27",
"20",
"12",
"35",
"43",
"22",
"13",
"23",
"1... | [
"nonn"
] | 21 | 1 | 2 | [
"A000040",
"A000720",
"A034694",
"A391765"
] | null | Ruud H.G. van Tol, Dec 19 2025 | 2025-12-27T18:28:34 | oeisdata/seq/A391/A391765.seq | 499150e473adfbc528e34d1773826e7a |
A391766 | Number of tetrahedra in the n X n black bishop graph. | [
"0",
"0",
"0",
"1",
"10",
"27",
"90",
"182",
"412",
"714",
"1324",
"2079",
"3414",
"5005",
"7574",
"10556",
"15064",
"20196",
"27576",
"35853",
"47298",
"59983",
"76978",
"95634",
"119988",
"146510",
"180388",
"217035",
"262990",
"312417",
"373422",
"438... | [
"nonn",
"easy",
"new"
] | 4 | 1 | 5 | null | null | Eric W. Weisstein, Dec 19 2025 | 2026-01-05T16:50:57 | oeisdata/seq/A391/A391766.seq | 141aa1e1fcf9fd11efaf5fc36ae1279b |
A391769 | The number of gaps in the set of positive integers which need at most n steps of the Collatz iteration to reach 1. | [
"0",
"0",
"1",
"2",
"3",
"4",
"6",
"7",
"10",
"14",
"20",
"26",
"35",
"45",
"57",
"73",
"94",
"121",
"159",
"202",
"255",
"322",
"411",
"520",
"658",
"836",
"1057",
"1339",
"1696",
"2143",
"2711",
"3429",
"4340",
"5494",
"6949",
"8788",
"11130"... | [
"nonn"
] | 18 | 0 | 4 | [
"A005186",
"A176014",
"A391769"
] | null | Markus Sigg, Dec 19 2025 | 2025-12-24T10:03:55 | oeisdata/seq/A391/A391769.seq | 7f12e3b348f14c404326293dc8a3f868 |
A391770 | Decimal expansion of log(8/(Pi^2)), negated. | [
"2",
"1",
"0",
"0",
"1",
"8",
"2",
"3",
"0",
"0",
"1",
"8",
"9",
"6",
"4",
"4",
"2",
"0",
"0",
"3",
"5",
"1",
"5",
"8",
"3",
"3",
"8",
"3",
"3",
"1",
"5",
"8",
"7",
"7",
"1",
"9",
"0",
"6",
"8",
"0",
"8",
"9",
"2",
"2",
"2",
"... | [
"nonn",
"cons",
"easy"
] | 9 | 0 | 1 | [
"A217739",
"A391770"
] | null | Paolo Xausa, Dec 19 2025 | 2025-12-20T06:31:01 | oeisdata/seq/A391/A391770.seq | 87a77d01225f7f06aaa9947c100d656d |
A391771 | Smallest number that is the sum of n > 2 consecutive primes and also the sum of n consecutive composites. | [
"23",
"102",
"53",
"112",
"341",
"150",
"187",
"594",
"1139",
"1336",
"423",
"484",
"611",
"2374",
"1439",
"1164",
"3181",
"2868",
"4325",
"1422",
"874",
"1552",
"7305",
"2050",
"3527",
"12534",
"18703",
"5118",
"3137",
"5980",
"4157",
"19156",
"9631",... | [
"nonn"
] | 29 | 3 | 1 | [
"A390613",
"A391771"
] | null | Jean-Marc Rebert, Dec 19 2025 | 2025-12-28T16:34:38 | oeisdata/seq/A391/A391771.seq | 15b61b4f5c113d6d2dcef6a681f9298a |
A391772 | a(n) is the least prime that can be written as (product - sum) of n distinct composite numbers. | [
"23",
"197",
"2131",
"24151",
"435397",
"3870653",
"46448561",
"1045094299",
"18811699079",
"362125209461",
"6320730931043",
"136949170175821",
"4213820620799791",
"86082335539199771",
"2336142152171519743",
"73213026376089599711",
"1708303948775423999689",
"61954489875588710399653... | [
"nonn"
] | 9 | 2 | 1 | [
"A391512",
"A391698",
"A391699",
"A391772"
] | null | Robert Israel, Dec 19 2025 | 2025-12-23T09:41:21 | oeisdata/seq/A391/A391772.seq | 3317ac2e97a924311fad873dca4f2be9 |
A391773 | a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 = k^3 has exactly n positive primitive integer solutions. | [
"6",
"41",
"87",
"219",
"606",
"492",
"2999",
"4351",
"5781",
"11023",
"19443",
"45897",
"74033",
"59049",
"139575",
"130321",
"255477",
"354225",
"468513",
"506169",
"455625",
"858171"
] | [
"nonn",
"more"
] | 8 | 1 | 1 | [
"A316359",
"A377444",
"A391773"
] | null | Zhining Yang, Dec 19 2025 | 2025-12-27T21:26:22 | oeisdata/seq/A391/A391773.seq | 524cb9b5a11f1d62b4500120991a6397 |
A391774 | Number of possibilities for the first n terms of the normalized chromatic difference sequence of the graph of a Young diagram. | [
"1",
"2",
"5",
"13",
"37",
"108",
"334"
] | [
"nonn",
"hard",
"more"
] | 10 | 1 | 2 | null | null | Timothy Y. Chow, Dec 19 2025 | 2025-12-28T16:09:03 | oeisdata/seq/A391/A391774.seq | 87bb50befd59803db63dffc4f318259a |
A391776 | Triangle read by rows: T(n,k) = number of heapable permutations of length n with exactly k 231 patterns. | [
"1",
"1",
"1",
"2",
"4",
"1",
"10",
"4",
"2",
"1",
"26",
"15",
"14",
"7",
"4",
"3",
"2",
"74",
"54",
"61",
"43",
"41",
"29",
"22",
"10",
"10",
"10",
"4",
"0",
"1",
"218",
"193",
"252",
"212",
"239",
"190",
"181",
"135",
"128",
"108",
"8... | [
"nonn",
"tabf",
"more",
"changed"
] | 26 | 0 | 4 | [
"A336282",
"A387705",
"A390832",
"A391697",
"A391776"
] | null | Manolopoulos Panagiotis, Dec 19 2025 | 2026-01-12T13:49:37 | oeisdata/seq/A391/A391776.seq | 123e775937b78771d696aa43b9e0d9b6 |
A391777 | Total number of 231 patterns in all heapable permutations of length n. | [
"0",
"0",
"0",
"0",
"1",
"11",
"107",
"1038",
"10522",
"113302",
"1302812",
"16015199",
"210235874",
"2941323511",
"43751523889",
"690175187973"
] | [
"nonn",
"more",
"new"
] | 14 | 0 | 6 | [
"A336282",
"A390832",
"A391697",
"A391776",
"A391777"
] | null | Manolopoulos Panagiotis, Dec 19 2025 | 2026-01-07T14:21:43 | oeisdata/seq/A391/A391777.seq | b6c6e50c6e229de094bc5776f539c33f |
A391778 | a(n) = n*(n-1)*(n- 2)^2*2^(n-4)/3. | [
"0",
"0",
"1",
"16",
"120",
"640",
"2800",
"10752",
"37632",
"122880",
"380160",
"1126400",
"3221504",
"8945664",
"24227840",
"64225280",
"167116800",
"427819008",
"1079574528",
"2689597440",
"6624378880",
"16148070400",
"38997590016",
"93381984256",
"221878681600",
... | [
"nonn",
"easy",
"new"
] | 10 | 1 | 4 | null | null | Eric W. Weisstein, Dec 19 2025 | 2026-01-08T02:50:25 | oeisdata/seq/A391/A391778.seq | 168e3bcf4280d956b1c6b000d2e88088 |
A391779 | a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(k+6,6) * binomial(2*k,2*(n-k)). | [
"1",
"14",
"154",
"2688",
"34608",
"387744",
"4189920",
"42410496",
"408280992",
"3787340480",
"33960764992",
"295868561408",
"2514525570816",
"20906787095040",
"170489979041280",
"1366489403252736",
"10783773983748864",
"83916508450048512",
"644759749272120832",
"4896753272486... | [
"nonn"
] | 13 | 0 | 2 | [
"A108486",
"A382473",
"A390849",
"A391723",
"A391779"
] | null | Seiichi Manyama, Dec 19 2025 | 2025-12-20T09:36:50 | oeisdata/seq/A391/A391779.seq | a6e41c407b0c13d571faf095b6ae80cb |
A391780 | Decimal expansion of (Pi/4) * arctan(1/(2*sqrt(2))). | [
"2",
"6",
"6",
"9",
"0",
"7",
"2",
"8",
"4",
"5",
"3",
"9",
"9",
"3",
"2",
"3",
"0",
"7",
"3",
"8",
"1",
"0",
"5",
"9",
"3",
"9",
"0",
"0",
"3",
"8",
"9",
"4",
"7",
"2",
"0",
"3",
"2",
"2",
"2",
"2",
"1",
"7",
"0",
"6",
"7",
"... | [
"nonn",
"cons"
] | 8 | 0 | 1 | [
"A000129",
"A003881",
"A188615",
"A391780"
] | null | Amiram Eldar, Dec 20 2025 | 2025-12-20T03:38:40 | oeisdata/seq/A391/A391780.seq | 11b0e619119eda19f4ef894058f0ed97 |
A391781 | Decimal expansion of Sum_{k>=1} eta(2*k) * Fibonacci(2*k) / 5^k, where eta is the Dirichlet eta function. | [
"4",
"1",
"1",
"6",
"1",
"2",
"0",
"2",
"3",
"7",
"9",
"5",
"6",
"8",
"7",
"4",
"6",
"2",
"7",
"5",
"0",
"5",
"4",
"3",
"2",
"1",
"7",
"7",
"2",
"4",
"7",
"3",
"4",
"9",
"9",
"1",
"2",
"3",
"1",
"2",
"2",
"4",
"3",
"8",
"7",
"... | [
"nonn",
"cons",
"changed"
] | 8 | 0 | 1 | [
"A000045",
"A001906",
"A350760",
"A391781",
"A391782"
] | null | Amiram Eldar, Dec 20 2025 | 2026-01-17T17:22:32 | oeisdata/seq/A391/A391781.seq | 1b0e4b73a6a5ad65e97b4c2fbcb2b2aa |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.