cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A341985 Number of ways to write n as an ordered sum of 6 primes (counting 1 as a prime).

Original entry on oeis.org

1, 6, 21, 50, 96, 156, 237, 336, 465, 596, 747, 882, 1077, 1260, 1536, 1736, 2067, 2286, 2761, 3030, 3627, 3842, 4578, 4806, 5826, 6000, 7167, 7116, 8562, 8430, 10318, 9906, 12093, 11396, 14286, 13386, 16868, 15270, 19242, 17180, 22218, 19536, 25393, 21750, 28680, 24456
Offset: 6

Views

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

Crossrefs

Cf. A008578, A280917, A283762, A340962, A341949, A341977, A341982, A341983, A341984, A341986, A341987, A341988, A341989.

Programs

  • Mathematica
    nmax = 51; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^6.

A341986 Number of ways to write n as an ordered sum of 7 primes (counting 1 as a prime).

Original entry on oeis.org

1, 7, 28, 77, 168, 308, 511, 785, 1155, 1603, 2142, 2723, 3430, 4207, 5202, 6216, 7497, 8729, 10451, 12061, 14350, 16205, 19033, 21182, 24934, 27482, 32109, 34587, 40139, 42714, 49791, 52290, 60718, 62699, 73297, 75278, 88571, 89488, 104993, 104482, 123760, 122066
Offset: 7

Views

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

Links

Crossrefs

Cf. A008578, A280917, A283762, A340963, A341950, A341978, A341982, A341983, A341984, A341985, A341987, A341988, A341989.

Programs

  • Maple
    b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 8)
    end:
a:= n-> coeff(b(n), x, 7):
seq(a(n), n=7..48);  # Alois P. Heinz, Feb 25 2021
  • Mathematica
    nmax = 48; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^7.

A341988 Number of ways to write n as an ordered sum of 9 primes (counting 1 as a prime).

Original entry on oeis.org

1, 9, 45, 156, 423, 954, 1887, 3384, 5661, 8935, 13446, 19332, 26838, 36126, 47691, 61668, 78696, 98631, 122665, 150516, 184230, 222438, 268146, 318564, 379383, 445572, 525942, 610344, 712872, 817290, 947166, 1075680, 1238148, 1391475, 1591236, 1773684, 2022241
Offset: 9

Views

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

Crossrefs

Cf. A008578, A280917, A283762, A340965, A341719, A341980, A341982, A341983, A341984, A341985, A341986, A341987, A341989.

Programs

  • Mathematica
    nmax = 45; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^9.

A341989 Number of ways to write n as an ordered sum of 10 primes (counting 1 as a prime).

Original entry on oeis.org

1, 10, 55, 210, 625, 1542, 3310, 6390, 11400, 19090, 30353, 46060, 67210, 94780, 130230, 174862, 230650, 298800, 382115, 482090, 603373, 746860, 918770, 1118100, 1355110, 1626742, 1949190, 2312380, 2740220, 3212640, 3769784, 4375900, 5092485, 5854680, 6758935, 7703112
Offset: 10

Views

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

Crossrefs

Cf. A008578, A280917, A283762, A340966, A341972, A341981, A341982, A341983, A341984, A341985, A341986, A341987, A341988.

Programs

  • Maple
    b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 11)
    end:
a:= n-> coeff(b(n), x, 10):
seq(a(n), n=10..45);  # Alois P. Heinz, Feb 25 2021
  • Mathematica
    nmax = 45; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^10.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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