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2025-04-28 00:58:08
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A357101
Decimal expansion of the real root of x^3 - 2*x^2 - 2.
[ "2", "3", "5", "9", "3", "0", "4", "0", "8", "5", "9", "7", "1", "7", "7", "6", "4", "2", "0", "7", "3", "0", "6", "6", "0", "3", "9", "2", "8", "0", "0", "5", "3", "2", "5", "5", "5", "3", "4", "6", "4", "8", "1", "2", "7", "8", "0", "6", "7", "6", "7", "2", "2", "8", "3", "7", "9", "7", "1", "4", "1", "2", "5", "1", "5", "8", "3", "8", "7", "5", "5", "8", "8", "9", "4", "4", "6", "5" ]
[ "nonn", "cons", "easy" ]
24
1
1
[ "A058265", "A357101" ]
null
Wolfdieter Lang, Sep 20 2022
2025-03-23T20:51:38
oeisdata/seq/A357/A357101.seq
4aad0ba953311c55a256e0158292f0f4
A357102
Decimal expansion of the real root of x^3 + 2*x - 2.
[ "7", "7", "0", "9", "1", "6", "9", "9", "7", "0", "5", "9", "2", "4", "8", "1", "0", "0", "8", "2", "5", "1", "4", "6", "3", "6", "9", "3", "0", "7", "0", "2", "6", "9", "6", "7", "2", "5", "5", "0", "5", "3", "1", "1", "9", "3", "6", "3", "3", "2", "8", "6", "1", "5", "1", "0", "0", "5", "9", "8", "4", "9", "2", "9", "7", "6", "7", "3", "5", "1", "0", "3", "2", "8", "2", "0" ]
[ "nonn", "cons", "easy" ]
16
0
1
[ "A273066", "A357102" ]
null
Wolfdieter Lang, Sep 20 2022
2023-10-27T10:32:51
oeisdata/seq/A357/A357102.seq
d190e8aa590c0986a61271d92e9ae023
A357103
Decimal expansion of the real root of x^3 - 3*x - 3.
[ "2", "1", "0", "3", "8", "0", "3", "4", "0", "2", "7", "3", "5", "5", "3", "6", "5", "3", "3", "1", "6", "4", "9", "4", "7", "3", "3", "2", "8", "2", "8", "9", "2", "8", "0", "9", "2", "4", "1", "9", "4", "1", "7", "0", "8", "3", "2", "3", "0", "2", "6", "8", "5", "1", "3", "7", "3", "4", "7", "4", "3", "0", "6", "2", "1", "2", "0", "9", "8", "3", "7", "1", "6", "4", "1", "4" ]
[ "nonn", "cons", "easy" ]
19
1
1
[ "A001622", "A357103", "A357104" ]
null
Wolfdieter Lang, Sep 20 2022
2023-09-16T20:58:55
oeisdata/seq/A357/A357103.seq
65b82a31780ca3f4751b40bc9268b96b
A357104
Decimal expansion of the real root of x^3 + 3*x - 1.
[ "3", "2", "2", "1", "8", "5", "3", "5", "4", "6", "2", "6", "0", "8", "5", "5", "9", "2", "9", "1", "1", "4", "7", "0", "7", "1", "0", "7", "0", "4", "0", "3", "1", "9", "8", "4", "9", "3", "1", "6", "4", "4", "3", "8", "2", "8", "9", "9", "5", "8", "4", "0", "0", "9", "1", "7", "8", "8", "4", "3", "9", "1", "1", "9", "0", "4", "2", "9", "6", "7", "6", "2", "3", "1", "2", "7", "8", "6" ]
[ "nonn", "cons", "easy" ]
20
0
1
[ "A001622", "A130880", "A332437", "A332438", "A357104" ]
null
Wolfdieter Lang, Sep 21 2022
2023-10-09T12:03:11
oeisdata/seq/A357/A357104.seq
f079d345861313de7b7e91b15316d72c
A357105
Decimal expansion of the real root of 2*x^3 - x^2 - 2.
[ "1", "1", "9", "7", "4", "2", "9", "3", "3", "6", "9", "3", "3", "0", "3", "2", "9", "7", "1", "5", "5", "9", "3", "0", "0", "2", "8", "7", "7", "9", "4", "7", "2", "1", "7", "3", "7", "1", "4", "0", "7", "5", "6", "0", "8", "6", "3", "2", "3", "9", "5", "8", "6", "4", "9", "3", "8", "1", "7", "5", "1", "3", "5", "8", "8", "5", "3", "3", "1", "5", "7", "0", "7", "3", "5", "6", "0", "9" ]
[ "nonn", "cons", "easy" ]
9
1
3
[ "A357105", "A357106" ]
null
Wolfdieter Lang, Sep 29 2022
2022-11-09T04:52:09
oeisdata/seq/A357/A357105.seq
32f89bac5769b5384a3915cb4a18d938
A357106
Decimal expansion of the real root of 2*x^3 + x^2 - 2.
[ "8", "5", "8", "0", "9", "4", "3", "2", "9", "4", "9", "6", "5", "5", "2", "7", "0", "6", "2", "5", "8", "7", "2", "5", "8", "5", "0", "9", "5", "8", "1", "8", "7", "5", "1", "5", "3", "0", "9", "0", "2", "6", "9", "2", "9", "2", "8", "6", "7", "1", "3", "6", "6", "6", "4", "9", "6", "1", "3", "7", "4", "1", "7", "4", "4", "7", "9", "2", "1", "4", "5", "5", "3", "0", "3", "3", "4", "8" ]
[ "nonn", "cons", "easy" ]
10
0
1
[ "A357105", "A357106" ]
null
Wolfdieter Lang, Sep 29 2022
2023-09-25T13:10:10
oeisdata/seq/A357/A357106.seq
b0dcf5df34e09104255b41123ab2d1ea
A357107
Decimal expansion of the real root of 2*x^3 - x - 2.
[ "1", "1", "6", "5", "3", "7", "3", "0", "4", "3", "0", "6", "2", "4", "1", "4", "7", "1", "6", "9", "5", "6", "3", "5", "8", "4", "3", "4", "5", "1", "7", "7", "9", "8", "0", "8", "2", "5", "4", "2", "8", "8", "7", "3", "1", "8", "8", "2", "0", "0", "4", "8", "6", "1", "3", "3", "4", "4", "2", "6", "6", "3", "1", "1", "6", "4", "8", "4", "4", "8", "4", "7", "1", "4", "0", "1", "1", "5" ]
[ "nonn", "cons", "easy" ]
6
1
3
[ "A357107", "A357108" ]
null
Wolfdieter Lang, Sep 29 2022
2022-10-13T13:04:14
oeisdata/seq/A357/A357107.seq
abfa2019898dbc8969bfdd85e5094adb
A357108
Decimal expansion of the real root of 2*x^3 + x - 2.
[ "8", "3", "5", "1", "2", "2", "3", "4", "8", "4", "8", "1", "3", "6", "6", "5", "1", "4", "2", "9", "1", "6", "2", "0", "0", "3", "8", "5", "9", "6", "7", "0", "2", "2", "9", "9", "1", "6", "5", "4", "1", "1", "4", "8", "7", "7", "8", "0", "4", "3", "3", "6", "0", "1", "9", "3", "6", "2", "7", "9", "7", "3", "1", "5", "3", "8", "5", "8", "9", "5", "1", "8", "1", "0", "9", "8", "0", "8" ]
[ "nonn", "cons", "easy" ]
6
0
1
[ "A357107", "A357108" ]
null
Wolfdieter Lang, Sep 29 2022
2022-10-13T13:04:22
oeisdata/seq/A357/A357108.seq
7b615b050b122f44af310a78557c413d
A357109
Decimal expansion of the real root of 2*x^3 - 2*x^2 - 1.
[ "1", "2", "9", "7", "1", "5", "6", "5", "0", "8", "1", "7", "7", "4", "2", "4", "3", "7", "2", "4", "6", "7", "8", "3", "0", "2", "2", "9", "8", "3", "7", "3", "1", "9", "5", "5", "5", "5", "3", "8", "0", "5", "5", "8", "1", "3", "7", "0", "3", "9", "6", "8", "2", "2", "8", "3", "6", "1", "5", "9", "4", "4", "3", "0", "8", "8", "4", "3", "8", "3", "9", "1", "4", "9", "5", "7", "0" ]
[ "nonn", "cons", "easy" ]
10
1
2
[ "A273065", "A357109" ]
null
Wolfdieter Lang, Sep 29 2022
2025-02-11T09:35:28
oeisdata/seq/A357/A357109.seq
9d1c9f48702571420dab11ea201c0545
A357110
Numbers k such that 1 + k^2 * 2^k + k^3 * 3^k is prime.
[ "2", "4", "6", "10", "12", "28", "30", "52", "60", "1170", "1292", "1882", "4760", "5160", "8388", "14652", "37700" ]
[ "nonn", "more" ]
32
1
1
[ "A058780", "A357110" ]
null
Enrico Masina, Sep 11 2022
2022-09-21T15:40:21
oeisdata/seq/A357/A357110.seq
29fffb583b7732090d16fde37a0880af
A357111
For n >= 1, a(n) = n / A076775(n).
[ "1", "1", "3", "1", "5", "3", "7", "1", "9", "1", "11", "3", "13", "7", "15", "1", "17", "9", "19", "1", "1", "11", "23", "3", "25", "13", "27", "7", "29", "3", "31", "1", "3", "17", "35", "9", "37", "19", "39", "1", "41", "1", "43", "11", "45", "23", "47", "3", "49", "5", "51", "13", "53", "27", "55", "7", "57", "29", "59", "3", "61", "31", "3", "1", "65", "3", "67", "17", "23", "7", "71", "9", "73", "37", "75" ]
[ "nonn", "base", "look" ]
23
1
3
[ "A000265", "A032533", "A076775", "A354837", "A357111" ]
null
Ctibor O. Zizka, Sep 11 2022
2022-09-26T02:05:34
oeisdata/seq/A357/A357111.seq
89405e2de557cb5832b1996fdae5fb93
A357112
a(n) = A035019(n)/6 for n > 0.
[ "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "2", "2", "1", "3", "2", "2", "2", "2", "1", "2", "2", "1", "2", "2", "1", "2", "4", "2", "2", "1", "2", "1", "2", "2", "2", "2", "1", "2", "2", "2", "4", "2", "1", "3", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "1", "2", "3", "2", "2", "2", "2", "4", "2", "2", "1", "2", "2", "2", "2", "1", "2", "4", "2", "1", "4", "2", "2", "4", "2", "2" ]
[ "nonn" ]
12
1
4
[ "A002324", "A003136", "A004016", "A343771", "A357112" ]
null
Hugo Pfoertner, Sep 11 2022
2023-08-04T23:16:40
oeisdata/seq/A357/A357112.seq
8fbcc8a584465f08ad885cfbaef7faf2
A357113
T(n,m) is the numerator of the resistance between two diametrically opposite nodes of a rectangular electric network of n*m quadratic cells in which all edges are replaced by one-ohm resistors, where T(n,m) is a triangle read by rows.
[ "1", "7", "3", "15", "121", "13", "45", "430", "2089", "47", "43", "1047", "37873", "2749", "1171", "239", "7148", "321249", "10499426", "2905619", "6385", "433", "33647", "59557", "156300899", "9176362943", "766114047605", "982871", "1157", "13971", "15887065", "1637345324", "120912032349", "25420198613182", "771357156007", "441083" ]
[ "nonn", "frac", "tabl" ]
18
1
2
[ "A093652", "A212045", "A212046", "A357113", "A357114", "A357115", "A357116" ]
null
Hugo Pfoertner, Sep 15 2022
2025-02-07T21:22:39
oeisdata/seq/A357/A357113.seq
e14a3ad372efaa47e365c9bd6ed5cee4
A357114
T(n,m) is the denominator of the resistance between two diametrically opposite nodes of a rectangular electric network of n*m quadratic meshes in which all edges are replaced by one-ohm resistors, where T(n,m) is a triangle read by rows.
[ "1", "5", "2", "8", "69", "7", "19", "209", "1023", "22", "15", "440", "16744", "1205", "495", "71", "2639", "128617", "4282081", "1169441", "2494", "112", "11067", "21728", "59292739", "3498175408", "287916805961", "360161", "265", "4142", "5317209", "579080689", "43600867640", "9153575734849", "273893674761", "153254" ]
[ "nonn", "frac", "tabl" ]
12
1
2
[ "A357113", "A357114" ]
null
Hugo Pfoertner, Sep 15 2022
2025-01-29T08:19:23
oeisdata/seq/A357/A357114.seq
3ad59d0876e076e75358bc588a9fc874
A357115
T(n,m) is the numerator of the resistance between two nodes located at the end of a side of length n of a rectangular electric network of n*m quadratic meshes in which all edges are replaced by one-ohm resistors, where T(n,m) is a square array read by descending antidiagonals.
[ "3", "11", "4", "41", "5", "13", "153", "26", "267", "26", "571", "68", "181", "192", "149", "2131", "89", "10609", "1506", "1171", "138", "7953", "466", "25059", "251", "155927", "246", "375", "29681", "1220", "3869723", "13852", "759435", "77948", "75255", "668", "110771", "1597", "1334085", "781778", "109897", "1949020", "982871", "24995", "3523" ]
[ "nonn", "frac", "tabl" ]
10
1
1
[ "A357113", "A357114", "A357115", "A357116" ]
null
Hugo Pfoertner, Sep 15 2022
2022-09-16T15:38:45
oeisdata/seq/A357/A357115.seq
56bb7d0ae4ae0c4a3bb7ffbfe01a078a
A357116
T(n,m) is the denominator of the resistance between two nodes located at the end of a side of length n of a rectangular electric network of n*m quadratic meshes in which all edges are replaced by one-ohm resistors, where T(n,m) is a square array read by descending antidiagonals.
[ "4", "15", "3", "56", "4", "7", "209", "21", "161", "11", "780", "55", "112", "95", "52", "2911", "72", "6603", "781", "495", "41", "10864", "377", "15617", "132", "70616", "91", "97", "40545", "987", "2412353", "7315", "352583", "31529", "24769", "153", "151316", "1292", "831712", "413351", "51480", "817991", "360161", "7412", "724" ]
[ "nonn", "frac", "tabl" ]
4
1
1
[ "A001353", "A001835", "A357115", "A357116" ]
null
Hugo Pfoertner, Sep 15 2022
2022-09-16T12:27:52
oeisdata/seq/A357/A357116.seq
e239da8c03fe18219a40630178c18091
A357117
Sums of two consecutive primes whose reversal is also the sum of two consecutive primes.
[ "5", "8", "24", "42", "210", "222", "240", "258", "288", "434", "480", "630", "696", "810", "828", "852", "882", "2100", "2112", "2580", "2610", "2640", "2728", "2740", "2780", "2886", "2904", "2992", "4056", "4092", "4224", "4260", "4268", "4296", "4340", "4410", "4458", "4476", "4554", "4680", "4688", "4698", "4860", "6078", "6090", "6300", "6336", "6378", "6504", "6690", "6720", "6744", "6798" ]
[ "nonn", "base" ]
25
1
1
[ "A001043", "A004086", "A162571", "A357117" ]
null
J. M. Bergot and Robert Israel, Sep 18 2022
2022-10-02T13:29:23
oeisdata/seq/A357/A357117.seq
8d68f80be53bd22ecdfa3f13de89aaf9
A357118
Numbers such that the first digit is the number of digits and the second digit is the number of distinct digits.
[ "322", "323", "4222", "4224", "4242", "4244", "4300", "4303", "4304", "4311", "4313", "4314", "4322", "4323", "4324", "4330", "4331", "4332", "4335", "4336", "4337", "4338", "4339", "4340", "4341", "4342", "4345", "4346", "4347", "4348", "4349", "4353", "4354", "4355", "4363", "4364", "4366", "4373", "4374", "4377", "4383", "4384", "4388", "4393", "4394", "4399" ]
[ "nonn", "base", "fini" ]
42
1
1
[ "A319678", "A357118" ]
null
Marc Morgenegg, Oct 17 2022
2022-11-12T01:36:44
oeisdata/seq/A357/A357118.seq
64224d3f4d5db7bab8e763538719586a
A357119
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} |Stirling1(n,k*j)|.
[ "1", "1", "0", "1", "1", "0", "1", "0", "2", "0", "1", "0", "1", "6", "0", "1", "0", "0", "3", "24", "0", "1", "0", "0", "1", "12", "120", "0", "1", "0", "0", "0", "6", "60", "720", "0", "1", "0", "0", "0", "1", "35", "360", "5040", "0", "1", "0", "0", "0", "0", "10", "226", "2520", "40320", "0", "1", "0", "0", "0", "0", "1", "85", "1645", "20160", "362880", "0", "1", "0", "0", "0", "0", "0", "15", "735", "13454", "181440", "3628800", "0" ]
[ "nonn", "tabl" ]
19
0
9
[ "A000007", "A000142", "A105752", "A357119", "A357293", "A357828" ]
null
Seiichi Manyama, Oct 17 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357119.seq
f81557f71d3d28d78ea0f8e4968e956a
A357120
Irregular triangle T(n, k), n > 0, k = 1..A278043(n); the n-th row contains, in ascending order, the terms in the greedy tribonacci representation of n.
[ "1", "2", "1", "2", "4", "1", "4", "2", "4", "7", "1", "7", "2", "7", "1", "2", "7", "4", "7", "1", "4", "7", "13", "1", "13", "2", "13", "1", "2", "13", "4", "13", "1", "4", "13", "2", "4", "13", "7", "13", "1", "7", "13", "2", "7", "13", "1", "2", "7", "13", "24", "1", "24", "2", "24", "1", "2", "24", "4", "24", "1", "4", "24", "2", "4", "24", "7", "24", "1", "7", "24", "2", "7", "24", "1", "2", "7", "24", "4", "7", "24" ]
[ "nonn", "tabf" ]
10
1
2
[ "A000073", "A035516", "A035517", "A275392", "A278038", "A278043", "A357120", "A357121" ]
null
Rémy Sigrist, Sep 12 2022
2022-09-14T08:26:26
oeisdata/seq/A357/A357120.seq
cdaa5fc73a12f030ff44a7972b83be60
A357121
Irregular triangle T(n, k), n > 0, k = 1..A352104(n); the n-th row contains, in ascending order, the terms in the lazy tribonacci representation of n.
[ "1", "2", "1", "2", "4", "1", "4", "2", "4", "1", "2", "4", "1", "7", "2", "7", "1", "2", "7", "4", "7", "1", "4", "7", "2", "4", "7", "1", "2", "4", "7", "2", "13", "1", "2", "13", "4", "13", "1", "4", "13", "2", "4", "13", "1", "2", "4", "13", "1", "7", "13", "2", "7", "13", "1", "2", "7", "13", "4", "7", "13", "1", "4", "7", "13", "2", "4", "7", "13", "1", "2", "4", "7", "13", "4", "24", "1", "4", "24", "2", "4", "24" ]
[ "nonn", "tabf" ]
10
1
2
[ "A000073", "A080843", "A112309", "A352103", "A352104", "A357120", "A357121" ]
null
Rémy Sigrist, Sep 12 2022
2022-09-14T08:26:21
oeisdata/seq/A357/A357121.seq
e2b2b9447d09acc2fb9a1b2828e06df9
A357122
Numbers k such that the sum of (q mod p) for pairs of primes p<q such that p+q=2*k is prime.
[ "4", "6", "7", "8", "9", "11", "13", "19", "24", "29", "31", "34", "39", "41", "44", "52", "59", "69", "73", "74", "81", "84", "96", "97", "102", "103", "107", "108", "113", "115", "118", "119", "120", "129", "135", "145", "153", "160", "164", "182", "207", "212", "230", "236", "243", "261", "264", "277", "285", "299", "306", "329", "337", "340", "342", "347", "358", "379", "386", "397", "410", "415", "420", "428", "434" ]
[ "nonn" ]
9
1
1
[ "A338984", "A357122" ]
null
J. M. Bergot and Robert Israel, Sep 12 2022
2022-10-02T13:29:33
oeisdata/seq/A357/A357122.seq
4522a950ec37e0d29c6d4ea635b1f2af
A357123
Number of sets S of size A066063(n) such that {1, 2, ..., n} is a subset of S + S.
[ "1", "1", "2", "2", "5", "5", "2", "1", "11", "8", "1", "1", "26", "16", "2", "1", "65", "39", "7", "5", "284", "183", "52", "31", "8", "3", "422", "243", "58", "31", "4", "2", "893", "475", "144", "79", "21", "11", "1", "1", "428", "233", "54", "29", "3", "2", "2034", "1180", "371", "213" ]
[ "nonn", "more" ]
16
1
3
[ "A066063", "A357123" ]
null
William Chang, Sep 12 2022
2022-10-15T08:10:16
oeisdata/seq/A357/A357123.seq
024133b5846aac4b61504b9613e3fa08
A357124
a(n) is the least k >= 1 such that A000045(n) + k*A000032(n) is prime, or -1 if there is no such k.
[ "1", "1", "2", "-1", "2", "6", "-1", "2", "8", "-1", "4", "2", "-1", "6", "2", "-1", "10", "4", "-1", "20", "2", "-1", "4", "44", "-1", "4", "56", "-1", "8", "22", "-1", "12", "16", "-1", "10", "2", "-1", "34", "8", "-1", "8", "16", "-1", "26", "10", "-1", "10", "14", "-1", "60", "4", "-1", "14", "28", "-1", "32", "16", "-1", "8", "20", "-1", "66", "44", "-1", "74", "12", "-1", "110", "40", "-1", "48", "6", "-1", "10", "4", "-1", "32", "34", "-1", "62" ]
[ "sign" ]
14
0
3
[ "A000032", "A000045", "A357124" ]
null
J. M. Bergot and Robert Israel, Sep 13 2022
2022-10-02T19:52:40
oeisdata/seq/A357/A357124.seq
0b3f110a61b473031d8f67e34d54414c
A357125
Positive integers n such that 2^(n-3) == -1 (mod n).
[ "1", "5", "4553", "46777", "82505", "4290773", "4492205", "4976429", "21537833", "21549349", "51127261", "56786089", "60296573", "80837773", "87761789", "94424465", "138644873", "168865001", "221395541", "255881453", "297460453", "305198249", "360306365", "562654205", "635374253", "673867253", "808333573", "1164757553", "1210317349" ]
[ "nonn" ]
12
1
2
[ "A006521", "A115976", "A245319", "A251603", "A276967", "A357125" ]
null
Max Alekseyev, Sep 13 2022
2025-02-08T18:34:22
oeisdata/seq/A357/A357125.seq
779788f5dd20d28aefed0e74eeeefffa
A357126
a(n) is the smallest positive integer k such that k > n and A071364(k) = A071364(n).
[ "3", "5", "9", "7", "10", "11", "27", "25", "14", "13", "20", "17", "15", "21", "81", "19", "50", "23", "28", "22", "26", "29", "40", "49", "33", "125", "44", "31", "42", "37", "243", "34", "35", "38", "100", "41", "39", "46", "56", "43", "66", "47", "45", "52", "51", "53", "80", "121", "75", "55", "63", "59", "250", "57", "88", "58", "62", "61", "84", "67", "65", "68", "729", "69", "70", "71", "76", "74", "78", "73", "200", "79", "77", "98" ]
[ "nonn" ]
99
2
1
[ "A000961", "A003961", "A065642", "A071364", "A081382", "A081761", "A357126" ]
null
Gleb Ivanov, Oct 26 2022
2023-02-17T07:39:53
oeisdata/seq/A357/A357126.seq
2d3e2fb28c764daee8670e823170e318
A357127
a(n) = A081257(n) if A081257(n) > n, otherwise a(n) = 1.
[ "7", "13", "7", "31", "43", "19", "73", "13", "37", "19", "157", "61", "211", "241", "1", "307", "1", "127", "421", "463", "1", "79", "601", "31", "37", "757", "271", "67", "1", "331", "151", "1123", "397", "97", "43", "67", "1483", "223", "547", "1723", "139", "631", "283", "109", "103", "61", "181", "1", "2551", "379", "919", "409", "2971", "79", "103", "3307", "163", "3541", "523", "97", "3907", "109", "73", "613" ]
[ "nonn" ]
21
2
1
[ "A081256", "A081257", "A108768", "A256148", "A357127" ]
null
Mohammed Bouras, Sep 13 2022
2022-10-15T21:16:10
oeisdata/seq/A357/A357127.seq
b634ebfc85ed42ba062e7c6fecabca72
A357128
a(n) is the least even number k > 2 such that the sum of the lower elements and the sum of the upper elements in the Goldbach partitions of k are both divisible by 2^n, but not both divisible by 2^(n+1).
[ "6", "4", "10", "16", "32", "468", "464", "3576", "14954", "96000", "403200" ]
[ "nonn", "more" ]
14
0
1
[ "A007814", "A185297", "A187129", "A357128" ]
null
J. M. Bergot and Robert Israel, Sep 13 2022
2025-03-23T20:52:45
oeisdata/seq/A357/A357128.seq
7acf6ef7aa761ce61670d3b437565ad5
A357129
Indices of records in A357052.
[ "0", "3", "4", "5", "7", "8", "9", "10", "14", "20", "22", "23", "26", "27", "32", "41", "51", "57", "82", "97", "116", "126", "153", "177", "181", "183", "216", "219" ]
[ "nonn", "more", "base" ]
61
1
2
[ "A357052", "A357129" ]
null
Jean-Marc Rebert, Sep 18 2022
2022-10-27T18:03:01
oeisdata/seq/A357/A357129.seq
7d4a0de051e44e71a1945881cf2cd6e2
A357130
a(n) = 2*n - (-1)^n*(1+(n mod 2)).
[ "4", "3", "8", "7", "12", "11", "16", "15", "20", "19", "24", "23", "28", "27", "32", "31", "36", "35", "40", "39", "44", "43", "48", "47", "52", "51", "56", "55", "60", "59", "64", "63", "68", "67", "72", "71", "76", "75", "80", "79", "84", "83", "88", "87", "92", "91", "96", "95", "100", "99", "104", "103", "108", "107", "112", "111", "116", "115", "120", "119", "124", "123", "128", "127", "132", "131", "136", "135", "140", "139", "144", "143", "148", "147", "152", "151", "156", "155", "160", "159" ]
[ "nonn", "easy" ]
51
1
1
[ "A005408", "A005843", "A168205", "A357130" ]
null
Zhi-Wei Sun, Sep 13 2022
2022-10-23T22:56:29
oeisdata/seq/A357/A357130.seq
70bd6f052136e419dbdc6c004d0c907e
A357131
Numbers m such that A010888(m) = A031347(m) = A031286(m) = A031346(m); only the least of the anagrams are considered.
[ "0", "137", "11126", "111134", "111278", "1111223", "11111447", "111112247", "1111122227", "111111111137", "11111111111126", "111111111111134", "1111111111111223", "111111111111111111111111111111111111111111111111111111111111111111111111111111111111278" ]
[ "nonn", "base" ]
58
1
2
[ "A010888", "A031286", "A031346", "A031347", "A064702", "A179239", "A239427", "A357131" ]
null
Mohammed Yaseen, Sep 14 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357131.seq
a802536d3e6cf56727dd229d0b034dd1
A357132
Numbers k such that the product of distinct digits of k equals the product of the prime divisors of k.
[ "1", "2", "3", "5", "6", "7", "135", "175", "735", "1176", "1715", "13122", "131712", "2333772" ]
[ "nonn", "base", "fini", "full" ]
22
1
2
[ "A002473", "A052382", "A067183", "A075048", "A238985", "A356981", "A357132" ]
null
Alexandru Petrescu, Sep 14 2022
2024-04-25T13:25:43
oeisdata/seq/A357/A357132.seq
28b348c9b3b5751babb5a315d82faf84
A357133
a(n) is the least prime that is the arithmetic mean of n consecutive primes.
[ "5", "127", "79", "101", "17", "269", "491", "727", "53", "23", "71", "181", "29", "31", "37", "43", "563", "331", "883", "283", "173", "307", "157", "113", "353", "571", "347", "89", "263", "139", "179", "1201", "281", "1553", "137", "5167", "347", "563", "2083", "2087", "491", "1867", "353", "463", "1973", "199", "599", "4373", "149", "9929", "277", "463", "1259", "251", "397", "2897", "787", "263", "2161" ]
[ "nonn" ]
16
3
1
[ "A006562", "A122531", "A126096", "A219478", "A357133" ]
null
J. M. Bergot and Robert Israel, Sep 14 2022
2022-10-02T20:01:41
oeisdata/seq/A357/A357133.seq
25ddfb15613204577724438a73f7522e
A357134
Take the k-th composition in standard order for each part k of the n-th composition in standard order; then set a(n) to be the index (in standard order) of the concatenation.
[ "0", "1", "2", "3", "3", "5", "6", "7", "4", "7", "10", "11", "7", "13", "14", "15", "5", "9", "14", "15", "11", "21", "22", "23", "12", "15", "26", "27", "15", "29", "30", "31", "6", "11", "18", "19", "15", "29", "30", "31", "20", "23", "42", "43", "23", "45", "46", "47", "13", "25", "30", "31", "27", "53", "54", "55", "28", "31", "58", "59", "31", "61", "62", "63", "7", "13", "22", "23", "19" ]
[ "nonn" ]
11
0
3
[ "A000120", "A001511", "A003963", "A029931", "A048896", "A058891", "A070939", "A096111", "A329395", "A333766", "A335404", "A357134", "A357135", "A357137", "A357180" ]
null
Gus Wiseman, Sep 24 2022
2022-09-26T22:02:10
oeisdata/seq/A357/A357134.seq
98c0569c73644e4fc7f8590ca2d1440f
A357135
Take the k-th composition in standard order for each part k of the n-th composition in standard order; then concatenate.
[ "1", "2", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "2", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "2", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "2", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1" ]
[ "nonn" ]
7
0
2
[ "A000120", "A001511", "A003963", "A029931", "A048896", "A058891", "A070939", "A096111", "A329395", "A333766", "A335404", "A357134", "A357135", "A357137", "A357139", "A357186", "A357187" ]
null
Gus Wiseman, Sep 26 2022
2022-09-27T09:00:12
oeisdata/seq/A357/A357135.seq
220550550b9d4774817317ae19cc82a9
A357136
Triangle read by rows where T(n,k) is the number of integer compositions of n with alternating sum k = 0..n. Part of the full triangle A097805.
[ "1", "0", "1", "1", "0", "1", "0", "2", "0", "1", "3", "0", "3", "0", "1", "0", "6", "0", "4", "0", "1", "10", "0", "10", "0", "5", "0", "1", "0", "20", "0", "15", "0", "6", "0", "1", "35", "0", "35", "0", "21", "0", "7", "0", "1", "0", "70", "0", "56", "0", "28", "0", "8", "0", "1", "126", "0", "126", "0", "84", "0", "36", "0", "9", "0", "1", "0", "252", "0", "210", "0", "120", "0", "45", "0", "10", "0", "1" ]
[ "nonn", "easy", "tabl" ]
13
0
8
[ "A000120", "A003242", "A011782", "A025047", "A032020", "A051159", "A070939", "A097805", "A103919", "A108044", "A114220", "A114901", "A124754", "A233564", "A238279", "A242882", "A260492", "A262046", "A262977", "A333489", "A335404", "A335405", "A344651", "A345167", "A348614", "A357136", "A357182", "A357183", "A357184", "A357185" ]
null
Gus Wiseman, Sep 30 2022
2023-11-02T07:54:50
oeisdata/seq/A357/A357136.seq
4810b192e8dbc077fc250fc486420ff9
A357137
Maximal run-length of the n-th composition in standard order; a(0) = 0.
[ "0", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "2", "1", "1", "2", "4", "1", "1", "1", "2", "1", "2", "1", "3", "1", "1", "2", "2", "2", "2", "3", "5", "1", "1", "1", "2", "2", "1", "1", "3", "1", "1", "3", "2", "1", "1", "2", "4", "1", "1", "1", "2", "1", "2", "1", "3", "2", "2", "2", "2", "3", "3", "4", "6", "1", "1", "1", "2", "1", "1", "1", "3", "1", "2", "2", "2", "1", "1", "2", "4", "1", "1", "1", "2", "2", "3", "2" ]
[ "nonn" ]
10
0
4
[ "A000120", "A001511", "A003754", "A029931", "A051903", "A051904", "A055396", "A056239", "A061395", "A070939", "A286470", "A333766", "A333768", "A356844", "A357136", "A357137", "A357138", "A357180", "A357181" ]
null
Gus Wiseman, Sep 18 2022
2022-09-24T14:59:28
oeisdata/seq/A357/A357137.seq
8afe43e83d48a81ed782ff14c2eaf381
A357138
Minimal run-length of the n-th composition in standard order; a(0) = 0.
[ "0", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "3", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "6", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
6
0
4
[ "A000120", "A001511", "A003754", "A029931", "A051903", "A051904", "A055396", "A056239", "A061395", "A070939", "A297173", "A333766", "A333768", "A356844", "A357136", "A357137", "A357138", "A357180", "A357181" ]
null
Gus Wiseman, Sep 18 2022
2022-09-24T14:58:24
oeisdata/seq/A357/A357138.seq
39fbb013c5f0c9820f14e8ea63b803e3
A357139
Take the weakly increasing prime indices of each prime index of n, then concatenate.
[ "1", "2", "1", "1", "1", "1", "1", "2", "3", "1", "1", "2", "1", "1", "1", "2", "4", "1", "1", "1", "1", "1", "2", "1", "1", "1", "3", "2", "2", "1", "2", "2", "1", "2", "1", "1", "1", "1", "1", "1", "3", "1", "2", "5", "1", "3", "4", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "2", "6", "1", "1", "1", "1", "4", "3", "1", "1", "2", "2", "2", "2", "3", "1", "1", "1", "1", "1", "2", "2", "1", "4", "1", "2" ]
[ "nonn", "tabf" ]
9
1
2
[ "A000720", "A000961", "A001221", "A001222", "A003963", "A007716", "A056239", "A058891", "A109082", "A275024", "A302242", "A302243", "A302505", "A302593", "A324926", "A325032", "A325033", "A325034", "A357134", "A357135", "A357139" ]
null
Gus Wiseman, Sep 29 2022
2022-09-29T22:05:36
oeisdata/seq/A357/A357139.seq
fe1a64fa4f4ee1dbc59a73230557812a
A357140
Number of n X n triangular (0,1)-matrices with exactly 2n entries equal to 1 and no zero rows or columns.
[ "1", "0", "0", "1", "26", "865", "39268", "2375965", "185974145", "18337523130", "2227232055239", "327003956573263", "57121908284696448", "11712143532463633752", "2786114854266411595229", "761208643373263480081077", "236761580851204534640426709", "83183218467008383189955036015" ]
[ "nonn" ]
5
0
5
[ "A137252", "A357140" ]
null
Alois P. Heinz, Sep 14 2022
2022-09-15T07:53:04
oeisdata/seq/A357/A357140.seq
979ec5056653781e22106a1d5a8a9c6c
A357141
Number of n X n triangular matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to 2n.
[ "1", "1", "6", "71", "1433", "44443", "1968580", "118159971", "9240555677", "913352224942", "111374887418013", "16428282185046946", "2883740893056526715", "594152447495864629867", "142006380268368661423424", "38973735372090120549251580", "12174162204364698538764222978", "4294569227671480526607187583713" ]
[ "nonn" ]
4
0
3
[ "A137251", "A357141" ]
null
Alois P. Heinz, Sep 14 2022
2022-09-15T07:59:52
oeisdata/seq/A357/A357141.seq
d850fc3b8f59a2a87129dffc18e813fd
A357142
Nonnegative numbers all of whose pairs of consecutive decimal digits are adjacent digits, where 9 and 0 are considered adjacent.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "21", "23", "32", "34", "43", "45", "54", "56", "65", "67", "76", "78", "87", "89", "90", "98", "101", "109", "121", "123", "210", "212", "232", "234", "321", "323", "343", "345", "432", "434", "454", "456", "543", "545", "565", "567", "654", "656", "676", "678", "765", "767", "787", "789", "876", "878", "890", "898", "901", "909" ]
[ "nonn", "base", "easy" ]
36
1
3
[ "A032981", "A033075", "A043089", "A048491", "A357142" ]
null
Ofer Zivony, Sep 14 2022
2022-12-09T23:04:32
oeisdata/seq/A357/A357142.seq
8fe126795df49e043cc3fb9d3bcbbe7d
A357143
a(n) is sum of the base-5 digits of n each raised to the number of digits of n in base 5.
[ "1", "2", "3", "4", "1", "2", "5", "10", "17", "4", "5", "8", "13", "20", "9", "10", "13", "18", "25", "16", "17", "20", "25", "32", "1", "2", "9", "28", "65", "2", "3", "10", "29", "66", "9", "10", "17", "36", "73", "28", "29", "36", "55", "92", "65", "66", "73", "92", "129", "8", "9", "16", "35", "72", "9", "10", "17", "36", "73", "16", "17", "24", "43", "80", "35", "36", "43", "62", "99", "72", "73", "80", "99", "136", "27" ]
[ "nonn", "base" ]
63
1
2
[ "A010346", "A101337", "A110592", "A151544", "A157714", "A357143", "A357954" ]
null
Francesco A. Catalanotti, Oct 26 2022
2023-10-26T20:17:21
oeisdata/seq/A357/A357143.seq
cd8dac26c57d381eaec231fa20f59b3d
A357144
Square array, A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = g(f(n) * f(k)) where f(m) = A002487(m)/A002487(m+1) and g is the inverse of f.
[ "0", "0", "0", "0", "1", "0", "0", "2", "2", "0", "0", "3", "8", "3", "0", "0", "4", "1", "1", "4", "0", "0", "5", "32", "15", "32", "5", "0", "0", "6", "14", "6", "6", "14", "6", "0", "0", "7", "4", "7", "256", "7", "4", "7", "0", "0", "8", "5", "9", "2", "2", "9", "5", "8", "0", "0", "9", "128", "63", "48", "35", "48", "63", "128", "9", "0", "0", "10", "6", "2", "1", "1", "1", "1", "2", "6", "10", "0", "0", "11", "56", "27", "2048", "47", "60", "47", "2048", "27", "56", "11", "0" ]
[ "nonn", "tabl" ]
8
0
8
[ "A002487", "A054429", "A354522", "A355090", "A357144" ]
null
Rémy Sigrist, Sep 15 2022
2022-09-18T12:37:49
oeisdata/seq/A357/A357144.seq
60b73746c62dbd5a0d0d55f374f61934
A357145
Decimal expansion of Sum_{n>=1} 1/A003422(n).
[ "1", "8", "8", "7", "2", "4", "2", "8", "7", "2", "1", "3", "9", "0", "0", "5", "4", "9", "5", "0", "5", "4", "3", "4", "3", "8", "2", "3", "3", "3", "9", "4", "6", "4", "2", "9", "2", "7", "2", "1", "0", "1", "8", "7", "3", "4", "7", "5", "8", "3", "1", "7", "1", "2", "9", "6", "6", "4", "6", "3", "8", "2", "5", "4", "4", "5", "0", "2", "5", "9", "4", "4", "9", "5", "0", "1", "0", "1", "0", "0", "3", "6", "2", "6", "9", "2", "7", "4", "0", "7", "7", "0", "5", "4", "3", "3", "5", "6", "0", "9", "6", "3", "8", "2", "4", "9" ]
[ "nonn", "cons" ]
16
1
2
[ "A001113", "A003422", "A357145" ]
null
Hafiz A. Aziz, Sep 15 2022
2022-09-30T09:55:17
oeisdata/seq/A357/A357145.seq
815dabebabb92f3a24451cb7f3639b09
A357146
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^(2*k)/(n - 2*k)!.
[ "1", "1", "1", "7", "49", "301", "6241", "74131", "1722337", "46346329", "1090339201", "48905462431", "1584330498961", "81705172522117", "4191355357015009", "223743062044497451", "16563314120270608321", "1027165911865738200241", "91346158358120706564097", "7395168869747626389974839" ]
[ "nonn" ]
11
0
4
[ "A353016", "A354436", "A356628", "A357146", "A357147" ]
null
Seiichi Manyama, Sep 15 2022
2022-09-15T11:44:40
oeisdata/seq/A357/A357146.seq
02eec4c9cb26bf542688d633a84cba9e
A357147
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^(3*k)/(n - 3*k)!.
[ "1", "1", "1", "1", "25", "481", "3241", "18481", "1332241", "44198785", "623190961", "15416707681", "1602405014761", "68167258954081", "1598025440555545", "134130467333575441", "14793638741719612321", "730659540435131811841", "34674365632872552887521", "5776415685538277157146305" ]
[ "nonn" ]
11
0
5
[ "A353017", "A354436", "A356629", "A357146", "A357147" ]
null
Seiichi Manyama, Sep 15 2022
2022-09-15T11:45:22
oeisdata/seq/A357/A357147.seq
8cd3fd96b0e426ab0b3f2282754b4a34
A357148
a(n) = A357082(n-1) + A357082(n).
[ "1", "3", "5", "7", "9", "15", "16", "15", "16", "24", "29", "32", "33", "29", "34", "29", "32", "36", "34", "42", "61", "64", "34", "32", "61", "64", "61", "64", "61", "64", "65", "72", "76", "64", "72", "85", "76", "64", "72", "82", "64", "72", "100", "104", "100", "91", "64", "72", "64", "72", "104", "100", "116", "127", "128", "129", "133", "128", "129", "128", "129", "128", "129" ]
[ "nonn" ]
16
1
2
[ "A357082", "A357148" ]
null
Michael De Vlieger, Sep 15 2022
2022-09-16T23:45:19
oeisdata/seq/A357/A357148.seq
944527e88a8524d8cf0996a2238174b3
A357149
a(n) = smallest missing number in A357082(k) for k = 0..n.
[ "1", "2", "3", "4", "5", "6", "6", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45", "45" ]
[ "nonn" ]
17
0
2
[ "A357082", "A357149" ]
null
Michael De Vlieger, Sep 15 2022
2022-11-18T03:39:44
oeisdata/seq/A357/A357149.seq
8b4c38cc4b5131a50e2330923ea87c02
A357150
Primitive terms in A357148.
[ "1", "3", "5", "7", "9", "15", "16", "24", "29", "32", "33", "34", "36", "42", "61", "64", "65", "72", "76", "82", "85", "91", "100", "104", "116", "127", "128", "129", "133", "144", "146", "153", "154", "169", "172", "179", "192", "209", "224", "256", "257", "258", "260", "262", "264", "270", "276", "281", "303", "322", "325", "339", "355", "356", "360", "400", "417", "418" ]
[ "nonn" ]
11
1
2
[ "A357082", "A357148", "A357150" ]
null
Michael De Vlieger, Sep 15 2022
2022-09-25T09:32:37
oeisdata/seq/A357/A357150.seq
f8baa4484fc64629ea2a07c787631d00
A357151
Coefficients in the power series A(x) such that: A(x) = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "1", "3", "13", "60", "299", "1586", "8697", "49117", "283437", "1664128", "9908903", "59694494", "363179981", "2228272706", "13771458148", "85655772108", "535759514193", "3367801361510", "21264574306632", "134804893426581", "857682458939905", "5474890014327326", "35053167752718368", "225046818744827456" ]
[ "nonn" ]
12
0
3
[ "A356783", "A357151", "A357152", "A357153", "A357154", "A357155" ]
null
Paul D. Hanna, Sep 16 2022
2022-09-16T22:01:44
oeisdata/seq/A357/A357151.seq
5100219756315c11ebb1174f0ce42619
A357152
Coefficients in the power series A(x) such that: A(x)^2 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "1", "4", "23", "147", "1022", "7529", "57605", "453691", "3653149", "29937140", "248865368", "2093488837", "17787701638", "152433293056", "1315973808843", "11434434212115", "99918928175263", "877543565096334", "7741838176253076", "68576621373325887", "609670801860847612", "5438211584097291663" ]
[ "nonn" ]
9
0
3
[ "A356783", "A357151", "A357152", "A357153", "A357154", "A357155" ]
null
Paul D. Hanna, Sep 16 2022
2022-09-16T22:02:32
oeisdata/seq/A357/A357152.seq
cc54f4b68dddec8f1547e69f50d4c5af
A357153
Coefficients in the power series A(x) such that: A(x)^3 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "1", "5", "36", "294", "2619", "24707", "242371", "2447978", "25284765", "265843662", "2835731692", "30612741292", "333824638817", "3671758248394", "40687442415206", "453801298156927", "5090406853194269", "57390539385386185", "649970717964393458", "7391173949517432182", "84358450717964077883" ]
[ "nonn" ]
9
0
3
[ "A356783", "A357151", "A357152", "A357153", "A357154", "A357155" ]
null
Paul D. Hanna, Sep 16 2022
2022-09-16T22:04:50
oeisdata/seq/A357/A357153.seq
2fa7b341cd51efb1fc2be4b590c6a94d
A357154
Coefficients in the power series A(x) such that: A(x)^4 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "1", "6", "52", "517", "5615", "64587", "772961", "9526304", "120084968", "1541062520", "20066028177", "264441631790", "3520463590183", "47274535397701", "639587090815124", "8709694025888081", "119288137354977880", "1642104576551818747", "22707897424654348214", "315300786621008803900" ]
[ "nonn" ]
9
0
3
[ "A356783", "A357151", "A357152", "A357153", "A357154", "A357155" ]
null
Paul D. Hanna, Sep 16 2022
2022-09-16T22:08:12
oeisdata/seq/A357/A357154.seq
4df820de15e641386fd224b2ef94d0c5
A357155
Coefficients in the power series A(x) such that: A(x)^5 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n.
[ "1", "1", "7", "71", "832", "10660", "144684", "2043814", "29736131", "442562703", "6706068107", "103109044005", "1604621459651", "25226987525340", "400062373648799", "6392118111706099", "102801779216363982", "1662854341556813731", "27034758217304814579", "441537893821034707720", "7240848432876171585800" ]
[ "nonn" ]
9
0
3
[ "A356783", "A357151", "A357152", "A357153", "A357154", "A357155" ]
null
Paul D. Hanna, Sep 16 2022
2022-09-16T22:10:56
oeisdata/seq/A357/A357155.seq
411e037d535c8b4a3a1e49090edefc24
A357156
Coefficients in the power series expansion of A(x) = Sum_{n=-oo..+oo} n*(n+1)*(n+2)/6 * x^(3*n) * (1 - x^n)^(n-2).
[ "1", "1", "1", "6", "1", "1", "16", "1", "1", "22", "1", "1", "71", "-63", "1", "127", "1", "-158", "211", "1", "1", "-117", "176", "1", "496", "-923", "1", "1277", "1", "-1727", "1002", "1", "1681", "-2021", "1", "1", "1821", "-1027", "1", "912", "1", "-7721", "11146", "1", "1", "-12571", "736", "15401", "4846", "-17016", "1", "-6389", "27457", "-20956", "7316", "1", "1", "-6486", "1", "1", "22177" ]
[ "sign" ]
9
3
4
[ "A291937", "A356774", "A356775", "A357156", "A357157" ]
null
Paul D. Hanna, Sep 22 2022
2022-09-23T03:11:13
oeisdata/seq/A357/A357156.seq
743429abeef6c88bc418825e7f5dc56a
A357157
Coefficients in the power series expansion of A(x) = Sum_{n=-oo..+oo} n*(n+1)*(n+2)*(n+3)/24 * x^(4*n) * (1 - x^n)^(n-2).
[ "1", "1", "1", "1", "7", "1", "1", "1", "22", "1", "1", "-19", "57", "1", "1", "1", "22", "1", "1", "1", "303", "-349", "1", "1", "463", "1", "-593", "1", "793", "1", "1", "-2204", "2584", "1", "1", "1", "-2287", "1", "3082", "1", "3004", "-8084", "1", "1", "14465", "-3674", "-14299", "1", "6189", "1", "22276", "-24023", "-2056", "1", "1", "1", "18714", "1", "1", "-34985", "24305", "-60059", "87517", "1", "20350" ]
[ "sign" ]
9
4
5
[ "A291937", "A356774", "A356775", "A357156", "A357157" ]
null
Paul D. Hanna, Sep 22 2022
2022-09-23T03:11:21
oeisdata/seq/A357/A357157.seq
d82efbe674e7bf377bad22ed880bf0cb
A357158
a(n) = coefficient of x^n in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n * A(x)^n.
[ "1", "2", "4", "28", "129", "784", "4547", "28474", "178947", "1160189", "7599423", "50580502", "339862004", "2306662818", "15774817084", "108652754620", "752854936635", "5244889634762", "36713446985136", "258094902741010", "1821402519619699", "12898863644572142", "91638273993427991", "652926934710002885" ]
[ "nonn" ]
13
0
2
null
null
Paul D. Hanna, Oct 05 2022
2022-12-03T12:04:33
oeisdata/seq/A357/A357158.seq
b1b78d0d3d3c4db5d87a335b981e4f0f
A357159
a(n) = coefficient of x^n in the power series A(x) such that: 0 = Sum_{n=-oo..+oo, n<>0} n * x^n * (1 - x^n)^(n-1) * A(x)^n, starting with a(0) = -1.
[ "-1", "-2", "-4", "-8", "-8", "-6", "40", "132", "400", "504", "76", "-4960", "-18528", "-56998", "-94176", "-58896", "617216", "2911128", "9741760", "19739472", "21657312", "-75073186", "-483271024", "-1800924184", "-4274295720", "-6374947674", "7150661892", "81254492928", "345397065128", "937137978804", "1717431001440" ]
[ "sign" ]
29
0
2
[ "A291937", "A357158", "A357159" ]
null
Paul D. Hanna, Oct 03 2022
2022-10-18T11:38:51
oeisdata/seq/A357/A357159.seq
29cfb99b401fd3987bc37e51b58138fa
A357160
Coefficients in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} x^(3*n+2) * (1 - x^(n-1))^(n+1) * A(x)^n.
[ "1", "1", "2", "8", "24", "88", "313", "1187", "4549", "17898", "71324", "288365", "1177729", "4856051", "20178061", "84427850", "355375253", "1503849591", "6394015744", "27301536104", "117020066991", "503313598572", "2171633107742", "9396938664272", "40769489510945", "177313714453588", "772906669281227", "3376119803594888" ]
[ "nonn" ]
9
0
3
[ "A356783", "A357160", "A357161", "A357162", "A357163", "A357164", "A357165" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-20T19:21:40
oeisdata/seq/A357/A357160.seq
c928ecef2e3c47af548294d8c1d64513
A357161
Coefficients in the power series A(x) such that: A(x) = Sum_{n=-oo..+oo} x^(3*n+2) * (1 - x^(n-1))^(n+1) * A(x)^n.
[ "1", "1", "3", "15", "71", "378", "2087", "12006", "70910", "428021", "2627731", "16358961", "103027423", "655236314", "4202210514", "27145925685", "176474644608", "1153679423108", "7579526316199", "50017854059557", "331390828183765", "2203548061830875", "14700363755114949", "98363233394747546" ]
[ "nonn" ]
10
0
3
[ "A357151", "A357160", "A357161", "A357162", "A357163", "A357164", "A357165" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-20T21:19:58
oeisdata/seq/A357/A357161.seq
c5a8b62afdd0dd19dcbaf1df9c214c15
A357162
Coefficients in the power series A(x) such that: A(x)^2 = Sum_{n=-oo..+oo} x^(3*n+2) * (1 - x^(n-1))^(n+1) * A(x)^n.
[ "1", "1", "4", "25", "162", "1160", "8731", "68364", "550707", "4535402", "38012170", "323168946", "2780229079", "24158457026", "211721412339", "1869239684558", "16609750957942", "148431230687412", "1333134683364035", "12027524448579488", "108951760865234373", "990555733683233240", "9035754580314840475" ]
[ "nonn" ]
9
0
3
[ "A357152", "A357160", "A357161", "A357162", "A357163", "A357164", "A357165" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-20T21:22:32
oeisdata/seq/A357/A357162.seq
e0de97f1c244dcb3cd079c7bfb766c30
A357163
Coefficients in the power series A(x) such that: A(x)^3 = Sum_{n=-oo..+oo} x^(3*n+2) * (1 - x^(n-1))^(n+1) * A(x)^n.
[ "1", "1", "5", "38", "313", "2834", "27088", "269380", "2757797", "28872568", "307696566", "3326835855", "36403128996", "402370063992", "4485931975701", "50386112677647", "569624341701738", "6476615022560400", "74013180802610161", "849642206122063571", "9793310961240979983", "113297108937174512275" ]
[ "nonn" ]
9
0
3
[ "A357153", "A357160", "A357161", "A357162", "A357163", "A357164", "A357165" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-20T21:21:33
oeisdata/seq/A357/A357163.seq
4c48e8f5fb654257a4a6f5c4dc8870a7
A357164
Coefficients in the power series A(x) such that: A(x)^4 = Sum_{n=-oo..+oo} x^(3*n+2) * (1 - x^(n-1))^(n+1) * A(x)^n.
[ "1", "1", "6", "54", "540", "5925", "68753", "830267", "10324947", "131329213", "1700614790", "22344117822", "297132512955", "3991542148276", "54086668396101", "738390401404546", "10146440406910223", "140227571720595241", "1947883865390758591", "27181029295364007844", "380838895427784827916" ]
[ "nonn" ]
9
0
3
[ "A357154", "A357160", "A357161", "A357162", "A357163", "A357164", "A357165" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-20T21:45:31
oeisdata/seq/A357/A357164.seq
69e19c23e39e50205fcc69a66315b120
A357165
Coefficients in the power series A(x) such that: A(x)^5 = Sum_{n=-oo..+oo} x^(3*n+2) * (1 - x^(n-1))^(n+1) * A(x)^n.
[ "1", "1", "7", "73", "859", "11083", "151369", "2151961", "31510682", "471993401", "7198166363", "111390268227", "1744706996712", "27606853938808", "440638645554932", "7086053148425023", "114700710907449375", "1867353232898846998", "30556409451787334011", "502291724376632138667", "8290605658533141188978" ]
[ "nonn" ]
9
0
3
[ "A357155", "A357160", "A357161", "A357162", "A357163", "A357164", "A357165" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-20T21:50:34
oeisdata/seq/A357/A357165.seq
b1c7c540117c1aec728a1afb53487426
A357166
If n appears in A357082, then a(n) is the unique k such that A357082(k) = n; otherwise a(n) = -1.
[ "0", "1", "2", "3", "4", "5", "7", "9", "23", "8", "6", "16", "11", "13", "49", "18", "14", "10", "15", "19", "12", "17", "47", "20", "24", "41", "22", "26", "34", "38", "28", "29", "31", "30", "27", "37", "33", "25", "21", "40", "32", "36", "46", "39", "35", "82", "51", "42", "78", "45", "48", "44", "74", "43", "52", "65", "67", "69", "50", "62", "60", "58", "53", "55", "87", "54", "56", "57" ]
[ "nonn", "look", "base" ]
12
0
3
[ "A357082", "A357166" ]
null
Rémy Sigrist, Sep 16 2022
2022-09-16T07:42:21
oeisdata/seq/A357/A357166.seq
774738f0e60b7dc6ca27c68e3587b774
A357167
Numbers k such that k and k+2 are both odd numbers whose prime factors are all prime-indexed primes.
[ "1", "3", "9", "15", "25", "31", "81", "83", "121", "123", "125", "153", "155", "177", "241", "275", "277", "295", "367", "459", "545", "561", "603", "615", "633", "737", "773", "991", "1003", "1023", "1087", "1199", "1201", "1203", "1215", "1375", "1383", "1395", "1409", "1411", "1413", "1445", "1681", "1845", "1851", "2025", "2075", "2099", "2125", "2319", "2417" ]
[ "nonn" ]
13
1
2
[ "A006450", "A076610", "A357167", "A357168", "A357169" ]
null
Amiram Eldar, Sep 16 2022
2022-09-19T07:23:11
oeisdata/seq/A357/A357167.seq
b42feefd13c2f556c4fbdd1d6967a7e1
A357168
Starts of runs of at least 3 consecutive odd numbers whose prime factors are all prime-indexed primes.
[ "1", "81", "121", "123", "153", "275", "1199", "1201", "1409", "1411", "2545", "3175", "4565", "5557", "5623", "6651", "7053", "8649", "11953", "15621", "16141", "16143", "20869", "22905", "28573", "36289", "39521", "51739", "52161", "56079", "56699", "56701", "63981", "76071", "77249", "79111", "105211", "125525", "144549", "153761", "167341" ]
[ "nonn" ]
12
1
2
[ "A006450", "A076610", "A357167", "A357168", "A357169" ]
null
Amiram Eldar, Sep 16 2022
2022-09-19T07:23:14
oeisdata/seq/A357/A357168.seq
bbb0725adfacf787250b138d1ddbc590
A357169
Starts of runs of at least 4 consecutive odd numbers whose prime factors are all prime-indexed primes.
[ "121", "1199", "1409", "16141", "56699", "474529", "695235", "1780713", "1917997", "6196985", "7209817", "7559673", "8084871", "11403485", "14409147", "22405711", "22608861", "23261179", "25803873", "27844653", "28729833", "31126321", "35664449", "43527369", "44425215", "48690429", "62579001", "63706967", "66780601" ]
[ "nonn" ]
9
1
1
[ "A006450", "A076610", "A357167", "A357168", "A357169" ]
null
Amiram Eldar, Sep 16 2022
2022-09-17T14:21:22
oeisdata/seq/A357/A357169.seq
21c085cf65086bd0dfb0aa2f03483b41
A357170
Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a prime power.
[ "3", "5", "7", "13", "19", "23", "29", "31", "37", "41", "43", "47", "53", "61", "67", "73", "79", "83", "89", "101", "103", "109", "113", "127", "131", "137", "139", "151", "157", "163", "167", "173", "181", "193", "199", "211", "223", "229", "233", "241", "251", "257", "263", "269", "271", "277", "281", "283", "293", "307", "311", "313", "317", "331", "337", "349", "353", "359", "367", "373" ]
[ "nonn", "easy" ]
14
1
1
[ "A000005", "A000040", "A061112", "A246655", "A353284", "A353285", "A353286", "A356833", "A357170", "A357175" ]
null
Claude H. R. Dequatre, Sep 16 2022
2022-11-02T07:51:53
oeisdata/seq/A357/A357170.seq
f50550d899f832bb9999042b03640f2a
A357171
a(n) is the number of divisors of n whose digits are in strictly increasing order (A009993).
[ "1", "2", "2", "3", "2", "4", "2", "4", "3", "3", "1", "6", "2", "4", "4", "5", "2", "6", "2", "4", "3", "2", "2", "8", "3", "4", "4", "6", "2", "6", "1", "5", "2", "4", "4", "9", "2", "4", "4", "5", "1", "6", "1", "3", "6", "4", "2", "10", "3", "4", "3", "5", "1", "7", "2", "8", "4", "4", "2", "8", "1", "2", "4", "5", "3", "4", "2", "6", "4", "6", "1", "11", "1", "3", "5", "5", "2", "8", "2", "6", "4", "2", "1", "9", "3", "2", "3", "4", "2", "9", "3", "5", "2", "3", "3", "10", "1", "5", "3", "5" ]
[ "nonn", "base" ]
36
1
2
[ "A009993", "A087990", "A160218", "A355302", "A355593", "A357171", "A357172", "A357173" ]
null
Bernard Schott, Sep 16 2022
2024-01-06T09:21:37
oeisdata/seq/A357/A357171.seq
c686336de5532fa4c94d3cd4a6a9544b
A357172
a(n) is the smallest integer that has exactly n divisors whose decimal digits are in strictly increasing order.
[ "1", "2", "4", "6", "16", "12", "54", "24", "36", "48", "72", "180", "144", "360", "336", "468", "504", "936", "1008", "1512", "2520", "3024", "5040", "6552", "7560", "22680", "13104", "19656", "49140", "105840", "39312", "78624", "98280", "248976", "334152", "196560", "393120", "668304", "1244880", "1670760", "1867320", "4520880", "3341520", "3734640" ]
[ "nonn", "base", "fini" ]
32
1
2
[ "A009993", "A087997", "A160218", "A355303", "A355594", "A357171", "A357172", "A357173" ]
null
Bernard Schott, Sep 16 2022
2022-09-17T14:11:36
oeisdata/seq/A357/A357172.seq
1705f4abcbd7f013f3c9eb3e8d9a9cd3
A357173
Positions of records in A357171, i.e., integers whose number of divisors whose decimal digits are in strictly increasing order sets a new record.
[ "1", "2", "4", "6", "12", "24", "36", "48", "72", "144", "336", "468", "504", "936", "1008", "1512", "2520", "3024", "5040", "6552", "7560", "13104", "19656", "39312", "78624", "98280", "196560", "393120", "668304", "1244880", "1670760", "1867320", "3341520", "3734640", "7469280", "22407840", "26142480", "31744440", "52284960", "63488880" ]
[ "nonn", "base", "fini" ]
20
1
2
[ "A009993", "A093036", "A160218", "A340548", "A355595", "A357171", "A357172", "A357173" ]
null
Bernard Schott, Sep 17 2022
2022-09-18T10:21:11
oeisdata/seq/A357/A357173.seq
f529a66c830e4259d15b5809808f743a
A357174
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^n/(n - 3*k)!.
[ "1", "1", "4", "27", "280", "5045", "134136", "4269223", "153188176", "6657007113", "371930499280", "25072409219891", "1872319689314856", "154583203638018493", "14784597239881491400", "1641532369038107170815", "201617558936011146124576", "26755058016106471234608017" ]
[ "nonn" ]
12
0
3
[ "A256016", "A353015", "A356834", "A357147", "A357174" ]
null
Seiichi Manyama, Sep 16 2022
2022-09-16T11:46:28
oeisdata/seq/A357/A357174.seq
caf3fca921dee4f9f8131f11a8c5c544
A357175
Primes p such that the minimum of the number of divisors among the numbers between p and NextPrime(p) is a cube.
[ "29", "41", "101", "137", "229", "281", "349", "439", "617", "641", "643", "739", "821", "823", "853", "967", "1087", "1423", "1429", "1447", "1549", "1579", "1597", "1693", "1697", "1783", "1877", "1999", "2081", "2131", "2237", "2239", "2293", "2377", "2381", "2539", "2617", "2657", "2683", "2693", "2713", "2749", "2791", "2801", "3079", "3319" ]
[ "nonn", "easy" ]
20
1
1
[ "A000005", "A000040", "A000578", "A061112", "A353284", "A353285", "A353286", "A356833", "A357170", "A357175" ]
null
Claude H. R. Dequatre, Sep 16 2022
2022-11-02T07:52:34
oeisdata/seq/A357/A357175.seq
6085e808f5b4afbfdb40507a401ee19a
A357176
a(n) is the least prime that is the n-th elementary symmetric function of the first k primes for some k.
[ "2", "31", "2101534937", "2927", "40361", "39075401846390482295581", "226026998201956974105518542793548663", "617651235401", "4325269278391458399931853204730438563", "12894795842691356733422939", "745410787149030809096434692201049325037186561467959704761393689387" ]
[ "nonn" ]
59
1
1
[ "A238146", "A357176" ]
null
Robert Israel, Sep 21 2022
2022-10-02T20:02:07
oeisdata/seq/A357/A357176.seq
96b3f52903c375e1ab2624ba8ef1f4ad
A357177
Prime indices of the Heegner numbers (A003173).
[ "0", "1", "2", "4", "5", "8", "14", "19", "38" ]
[ "nonn", "fini", "full" ]
19
1
3
[ "A000720", "A003173", "A357177" ]
null
Alexander R. Povolotsky, Sep 16 2022
2022-09-17T19:30:07
oeisdata/seq/A357/A357177.seq
7a8a19668d75399ee71a9738da41b96d
A357178
First differences of cubes of triangular numbers.
[ "0", "1", "26", "189", "784", "2375", "5886", "12691", "24704", "44469", "75250", "121121", "187056", "279019", "404054", "570375", "787456", "1066121", "1418634", "1858789", "2402000", "3065391", "3867886", "4830299", "5975424", "7328125", "8915426", "10766601", "12913264", "15389459", "18231750", "21479311", "25174016", "29360529" ]
[ "nonn", "easy" ]
49
0
3
[ "A000217", "A000578", "A003215", "A059827", "A168364", "A357178" ]
null
Kelvin Voskuijl, Sep 16 2022
2024-12-21T17:58:27
oeisdata/seq/A357/A357178.seq
9762fff2d34c106c472a35fc46c13727
A357179
Expansion of Product_{k>=1} (1 - x^k)^Fibonacci(k).
[ "1", "-1", "-1", "-1", "-1", "0", "-1", "2", "1", "5", "6", "14", "15", "32", "40", "64", "86", "131", "166", "237", "287", "362", "389", "368", "149", "-339", "-1477", "-3680", "-7827", "-15245", "-28270", "-50493", "-87886", "-149827", "-250966", "-414542", "-675741", "-1089267", "-1736640", "-2741788", "-4284837", "-6632751", "-10162683", "-15412613", "-23110653", "-34236290" ]
[ "sign" ]
10
0
8
[ "A000045", "A166861", "A261050", "A357179", "A357475" ]
null
Ilya Gutkovskiy, Oct 02 2022
2022-10-23T23:59:45
oeisdata/seq/A357/A357179.seq
5f212b7711e33998e67f1c10d85c9dcc
A357180
First run-length of the n-th composition in standard order.
[ "0", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1", "2", "4", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "2", "3", "5", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "3", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "3", "3", "4", "6", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "2" ]
[ "nonn" ]
9
0
4
[ "A000120", "A001511", "A003754", "A029931", "A051903", "A061395", "A065120", "A067029", "A070939", "A071178", "A124767", "A286470", "A329395", "A333766", "A333768", "A333769", "A353847", "A356841", "A356844", "A357134", "A357135", "A357136", "A357137", "A357138", "A357180", "A357181" ]
null
Gus Wiseman, Sep 24 2022
2022-09-26T08:20:37
oeisdata/seq/A357/A357180.seq
d3dc571c3c2464dff0a18f0118969e02
A357181
Last run-length of the n-th composition in standard order.
[ "0", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "2", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "2", "1", "1", "1", "5", "1", "1", "1", "2", "2", "1", "1", "3", "1", "1", "3", "2", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "2", "1", "1", "1", "6", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "2", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1" ]
[ "nonn" ]
5
0
4
[ "A000120", "A001511", "A003754", "A029931", "A051903", "A061395", "A065120", "A067029", "A070939", "A071178", "A124767", "A286470", "A329395", "A333766", "A333768", "A333769", "A353847", "A356841", "A356844", "A357134", "A357135", "A357136", "A357137", "A357138", "A357180", "A357181" ]
null
Gus Wiseman, Sep 24 2022
2022-09-26T08:20:30
oeisdata/seq/A357/A357181.seq
6896d680280b7a6400c442aa01040d63
A357182
Number of integer compositions of n with the same length as their alternating sum.
[ "1", "1", "0", "0", "1", "3", "1", "4", "6", "20", "13", "48", "50", "175", "141", "512", "481", "1719", "1491", "5400", "4929", "17776", "15840", "57420", "52079", "188656", "169989", "617176", "559834", "2033175", "1842041", "6697744", "6085950", "22139780", "20123989", "73262232", "66697354", "242931321", "221314299", "806516560" ]
[ "nonn" ]
17
0
6
[ "A000120", "A003242", "A011782", "A025047", "A032020", "A070939", "A106356", "A114220", "A114901", "A124754", "A131044", "A178470", "A233564", "A238279", "A242882", "A261983", "A262046", "A262977", "A301987", "A333489", "A335404", "A335405", "A345167", "A348614", "A357136", "A357182", "A357183", "A357184", "A357189" ]
null
Gus Wiseman, Sep 28 2022
2022-09-29T12:55:57
oeisdata/seq/A357/A357182.seq
293822f94be8749c75feef8bb2311d23
A357183
Number of integer compositions with the same length as the absolute value of their alternating sum.
[ "1", "1", "0", "0", "2", "3", "2", "5", "12", "22", "26", "58", "100", "203", "282", "616", "962", "2045", "2982", "6518", "9858", "21416", "31680", "69623", "104158", "228930", "339978", "751430", "1119668", "2478787", "3684082", "8182469", "12171900", "27082870", "40247978", "89748642", "133394708", "297933185", "442628598", "990210110" ]
[ "nonn" ]
13
0
5
[ "A000120", "A003242", "A011782", "A025047", "A032020", "A070939", "A106356", "A114220", "A114901", "A124754", "A131044", "A178470", "A233564", "A238279", "A242882", "A261983", "A262046", "A262977", "A301987", "A333489", "A335404", "A335405", "A345167", "A348614", "A357136", "A357182", "A357183", "A357185", "A357189" ]
null
Gus Wiseman, Sep 28 2022
2022-09-29T12:56:36
oeisdata/seq/A357/A357183.seq
64a13b11d77a3c9a0f6da8a9b4fdef8a
A357184
Numbers k such that the k-th composition in standard order has the same length as its alternating sum.
[ "0", "1", "9", "19", "22", "28", "34", "69", "74", "84", "104", "132", "135", "141", "153", "177", "225", "265", "271", "274", "283", "286", "292", "307", "310", "316", "328", "355", "358", "364", "376", "400", "451", "454", "460", "472", "496", "520", "523", "526", "533", "538", "553", "562", "593", "610", "673", "706", "833", "898", "1041", "1047", "1053", "1058" ]
[ "nonn" ]
13
1
3
[ "A000120", "A003242", "A011782", "A025047", "A032020", "A070939", "A114220", "A114901", "A124754", "A178470", "A233564", "A238279", "A242882", "A262046", "A262977", "A301987", "A333489", "A335404", "A335405", "A345167", "A348614", "A357136", "A357182", "A357183", "A357184", "A357189" ]
null
Gus Wiseman, Sep 28 2022
2022-09-29T12:57:02
oeisdata/seq/A357/A357184.seq
e4fcb1adc04bbad7b81069761dd2bcc3
A357185
Numbers k such that the k-th composition in standard order has the same length as the absolute value of its alternating sum.
[ "0", "1", "9", "12", "19", "22", "28", "34", "40", "69", "74", "84", "97", "104", "132", "135", "141", "144", "153", "177", "195", "198", "204", "216", "225", "240", "265", "271", "274", "283", "286", "292", "307", "310", "316", "321", "328", "355", "358", "364", "376", "386", "400", "451", "454", "460", "472", "496", "520", "523", "526", "533", "538", "544", "553" ]
[ "nonn" ]
10
1
3
[ "A000120", "A003242", "A011782", "A025047", "A032020", "A070939", "A114220", "A114901", "A124754", "A178470", "A233564", "A238279", "A242882", "A262046", "A262977", "A301987", "A333489", "A335404", "A335405", "A345167", "A348614", "A357136", "A357183", "A357184", "A357185" ]
null
Gus Wiseman, Sep 28 2022
2022-09-29T12:57:51
oeisdata/seq/A357/A357185.seq
26c02b2a9fc0dc1e00b157158ea050f3
A357186
Take the k-th composition in standard order for each part k of the n-th composition in standard order, then add up everything.
[ "0", "1", "2", "2", "2", "3", "3", "3", "3", "3", "4", "4", "3", "4", "4", "4", "3", "4", "4", "4", "4", "5", "5", "5", "4", "4", "5", "5", "4", "5", "5", "5", "3", "4", "5", "5", "4", "5", "5", "5", "5", "5", "6", "6", "5", "6", "6", "6", "4", "5", "5", "5", "5", "6", "6", "6", "5", "5", "6", "6", "5", "6", "6", "6", "3", "4", "5", "5", "5", "6", "6", "6", "5", "5", "6", "6", "5", "6", "6", "6", "5", "6", "6", "6", "6", "7", "7" ]
[ "nonn" ]
6
0
3
[ "A000120", "A001511", "A003963", "A029837", "A029931", "A048896", "A058891", "A070939", "A096111", "A133494", "A325033", "A329395", "A333766", "A335404", "A357135", "A357137", "A357186", "A357187" ]
null
Gus Wiseman, Sep 28 2022
2022-09-29T07:42:03
oeisdata/seq/A357/A357186.seq
94195500faf2e1953df168b88e641963
A357187
First differences A357186 = "Take the k-th composition in standard order for each part k of the n-th composition in standard order, then add up everything."
[ "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "1", "0", "0", "-1", "0", "1", "0", "-1", "1", "0", "0", "-2", "1", "1", "0", "-1", "1", "0", "0", "0", "0", "1", "0", "-1", "1", "0", "0", "-2", "1", "0", "0", "0", "1", "0", "0", "-1", "0", "1", "0", "-1", "1", "0", "0", "-3", "1", "1", "0", "0", "1", "0", "0", "-1", "0", "1", "0", "-1", "1", "0", "0", "-1", "1", "0" ]
[ "sign" ]
10
0
32
[ "A000120", "A029837", "A029931", "A048896", "A052955", "A058891", "A070939", "A133494", "A325033", "A333766", "A357134", "A357135", "A357137", "A357186", "A357187", "A357458" ]
null
Gus Wiseman, Sep 28 2022
2022-09-29T22:05:42
oeisdata/seq/A357/A357187.seq
fd1503c9bed5590f98a24d2ae98ac189
A357188
Numbers with (WLOG adjacent) prime indices x <= y such that the greatest prime factor of x is greater than the least prime factor of y.
[ "35", "65", "70", "95", "105", "130", "140", "143", "145", "169", "175", "185", "190", "195", "209", "210", "215", "245", "247", "253", "260", "265", "280", "285", "286", "290", "305", "315", "319", "323", "325", "338", "350", "355", "370", "377", "380", "385", "390", "391", "395", "407", "418", "420", "429", "430", "435", "445", "455", "473", "475", "481", "490" ]
[ "nonn" ]
8
1
1
[ "A000720", "A000961", "A001221", "A001222", "A003963", "A007716", "A056239", "A275024", "A302242", "A302243", "A302505", "A324926", "A325032", "A325034", "A357139", "A357188" ]
null
Gus Wiseman, Sep 30 2022
2022-09-30T07:50:43
oeisdata/seq/A357/A357188.seq
294b3c684eb3bf7be5994b4f7371491d
A357189
Number of integer partitions of n with the same length as alternating sum.
[ "1", "1", "0", "0", "1", "1", "1", "2", "2", "4", "3", "5", "6", "9", "9", "13", "16", "23", "23", "34", "37", "54", "54", "78", "84", "120", "121", "170", "182", "252", "260", "358", "379", "517", "535", "725", "764", "1030", "1064", "1427", "1494", "1992", "2059", "2733", "2848", "3759", "3887", "5106", "5311", "6946", "7177", "9345", "9701", "12577", "12996", "16788" ]
[ "nonn" ]
11
0
8
[ "A000009", "A000041", "A001055", "A004526", "A025047", "A051159", "A070939", "A097805", "A103919", "A114220", "A131044", "A262046", "A262977", "A301987", "A335405", "A344651", "A357136", "A357182", "A357183", "A357184", "A357189", "A357485", "A357486", "A357487" ]
null
Gus Wiseman, Sep 30 2022
2022-10-01T19:23:09
oeisdata/seq/A357/A357189.seq
7638ddb08cd30bec74dbd789faeb645a
A357190
a(n) is the least prime p such that A234575(p, A007953(p)) is the n-th power of a prime.
[ "17", "13", "131", "107", "383", "613", "43607", "1021", "334403", "26099", "40637", "138967", "212867", "360049", "502210997", "2227399", "5682166613", "7339303", "13630913", "35650627", "92273957", "142605709", "4424729404133", "671087119", "42364430471219", "2684353351", "404156666702231", "10737417109", "4872756792902003" ]
[ "nonn", "base" ]
57
1
1
[ "A007953", "A234575", "A357190" ]
null
J. M. Bergot and Robert Israel, Oct 25 2022
2022-11-09T19:10:08
oeisdata/seq/A357/A357190.seq
eead926ee820896d5aa97f9a5f4426f5
A357191
a(n) = n! * Sum_{k=0..floor(n/2)} k^n/k!.
[ "1", "0", "2", "6", "216", "2040", "111240", "2164680", "159391680", "5247305280", "491431600800", "24437592194400", "2800955712804480", "195393943295591040", "26699221909806526080", "2479967110139382864000", "396503602252401676032000", "47167550656581451928832000" ]
[ "nonn" ]
9
0
3
[ "A256016", "A352981", "A357191", "A357192", "A357193" ]
null
Seiichi Manyama, Sep 17 2022
2022-09-17T08:44:53
oeisdata/seq/A357/A357191.seq
2becb4dfdb147fc49b5d11f264073a05
A357192
a(n) = n! * Sum_{k=0..floor(n/3)} k^n/k!.
[ "1", "0", "0", "6", "24", "120", "23760", "327600", "5201280", "1283688000", "37574409600", "1219438281600", "378254710310400", "19092171351052800", "1045282110435763200", "394211859168070944000", "30499777423295212032000", "2523689643597315088896000", "1125362204955051396299366400" ]
[ "nonn" ]
10
0
4
[ "A256016", "A352982", "A357191", "A357192", "A357194" ]
null
Seiichi Manyama, Sep 17 2022
2022-09-17T08:50:09
oeisdata/seq/A357/A357192.seq
6dd39f2368114d5f1b3c3c06f3a2e21a
A357193
a(n) = n! * Sum_{k=0..floor(n/2)} k^(2*n)/k!.
[ "1", "0", "2", "6", "3096", "61560", "65248200", "4058986680", "7506140268480", "1062517243193280", "3052268000677879200", "822543740977513816800", "3395913346775619237617280", "1553795963458841732838848640", "8727392877498334693600263757440" ]
[ "nonn" ]
11
0
3
[ "A256016", "A352983", "A357191", "A357193", "A357194" ]
null
Seiichi Manyama, Sep 17 2022
2022-09-17T08:48:26
oeisdata/seq/A357/A357193.seq
e64e3ed0a89f34cc706b25aabdba0d31
A357194
a(n) = n! * Sum_{k=0..floor(n/3)} k^(3*n)/k!.
[ "1", "0", "0", "6", "24", "120", "94372560", "5284828080", "338228714880", "461220488356944960", "124524904888012809600", "36983489578531184304000", "94262861823240343196388902400", "78420937396722501660156363686400", "70262981254649802508019882162611200" ]
[ "nonn" ]
12
0
4
[ "A256016", "A352984", "A357192", "A357193", "A357194" ]
null
Seiichi Manyama, Sep 17 2022
2022-09-17T08:48:43
oeisdata/seq/A357/A357194.seq
45189ed0e3284dda816d935539b749ac
A357195
a(n) is the smallest palindrome of the form k*(2*n+k-1)/2 where k is a positive integer.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "33", "11", "969", "222", "99", "66", "33", "242", "282", "424", "161", "66", "22", "212", "252", "646", "171", "55", "252", "414", "555", "525", "99", "33", "474", "1001", "111", "5005", "77", "484", "1111", "1881", "414", "808", "44", "606", "141", "404", "303", "99", "101", "555", "444", "333", "222", "55", "171", "484" ]
[ "base", "nonn" ]
15
1
2
[ "A002113", "A020485", "A262038", "A357195" ]
null
Gleb Ivanov, Sep 17 2022
2022-10-29T12:00:59
oeisdata/seq/A357/A357195.seq
1e7babbe6409127f3f160df0b68d21f0
A357196
Number of regions in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts.
[ "1", "7", "25", "55", "97", "151", "217", "295", "385", "475", "601", "715", "865", "1015", "1159", "1351", "1537", "1735", "1945", "2131", "2401", "2647", "2905", "3115", "3457", "3751", "4057", "4357", "4705", "5005", "5401", "5767", "6133", "6535", "6925", "7303", "7777", "8215", "8653", "9025", "9601", "10051", "10585", "11071", "11587", "12151", "12697", "13171", "13825", "14395", "14989" ]
[ "nonn" ]
21
0
2
[ "A227776", "A331931", "A356984", "A357058", "A357196", "A357197", "A357198" ]
null
Scott R. Shannon, Sep 17 2022
2023-10-11T14:42:01
oeisdata/seq/A357/A357196.seq
5cbbb3ac7d509b59752772aae0b7d24b
A357197
Number of vertices in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts.
[ "6", "12", "30", "60", "102", "156", "222", "300", "390", "468", "606", "708", "870", "1020", "1152", "1356", "1542", "1740", "1950", "2112", "2406", "2652", "2910", "3072", "3462", "3756", "4062", "4350", "4710", "4974", "5406", "5772", "6126", "6540", "6918", "7260", "7782", "8220", "8646", "8946", "9606", "10032", "10590", "11052", "11568", "12156", "12702", "13116", "13830", "14388" ]
[ "nonn" ]
14
0
1
[ "A330846", "A357007", "A357060", "A357196", "A357197", "A357198" ]
null
Scott R. Shannon, Sep 17 2022
2022-09-18T12:37:34
oeisdata/seq/A357/A357197.seq
a1ae58d58b499169b1436db968ac5ed2
A357198
Number of edges in a hexagon when n internal hexagons are drawn between the 6n points that divide each side into n+1 equal parts.
[ "6", "18", "54", "114", "198", "306", "438", "594", "774", "942", "1206", "1422", "1734", "2034", "2310", "2706", "3078", "3474", "3894", "4242", "4806", "5298", "5814", "6186", "6918", "7506", "8118", "8706", "9414", "9978", "10806", "11538", "12258", "13074", "13842", "14562", "15558", "16434", "17298", "17970", "19206", "20082", "21174", "22122", "23154", "24306", "25398", "26286" ]
[ "nonn" ]
13
0
1
[ "A330845", "A357008", "A357061", "A357196", "A357197", "A357198" ]
null
Scott R. Shannon, Sep 17 2022
2022-09-18T12:37:28
oeisdata/seq/A357/A357198.seq
7c0d75fba431ee613b0b0257906a8090
A357199
Primes p such that (5*p+2)/3 is the square of a prime.
[ "2", "5", "29", "101", "173", "317", "821", "1109", "2693", "4133", "6869", "9677", "11261", "17957", "22349", "29837", "32573", "60293", "68141", "83477", "128621", "164117", "186149", "190181", "221069", "225461", "343829", "406397", "440669", "467813", "526781", "561053", "579773", "716789", "748613", "845381", "853949", "888653", "1131077", "1214957", "1326701", "1647389" ]
[ "nonn" ]
24
1
1
null
null
J. M. Bergot and Robert Israel, Sep 18 2022
2022-10-02T13:49:35
oeisdata/seq/A357/A357199.seq
49e5677a1f27081aca11b4ef447ae97d
A357200
Coefficients in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} x^n * (1 - x^(n+1))^(n+1) * A(x)^n.
[ "1", "1", "0", "0", "-7", "-3", "-17", "52", "51", "384", "-227", "-52", "-6311", "-2722", "-18733", "79229", "67453", "620385", "-619315", "85796", "-13137380", "-595833", "-43282243", "205480697", "66895157", "1551910768", "-2300631561", "1546386060", "-36481481081", "15982958026", "-135266506195", "652843485153" ]
[ "sign" ]
7
0
5
[ "A356783", "A357160", "A357200", "A357201", "A357202", "A357203", "A357204", "A357205" ]
null
Paul D. Hanna, Sep 17 2022
2022-09-18T12:36:49
oeisdata/seq/A357/A357200.seq
34b07f629193fb2ab3b9dbf9dcbddc8d