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.

Previous Showing 11-13 of 13 results.

A129491 Digital sum of the 2^n-th partition number.

Original entry on oeis.org

1, 2, 5, 4, 6, 24, 22, 34, 83, 120, 152, 145, 286, 477, 561, 796, 1271, 1639, 2471, 3598, 5114, 7221, 10283, 14315, 20585, 29110, 40890, 58834, 82319, 115690, 164128, 232044, 328463, 462853, 657811, 927235, 1311605, 1855787, 2629927, 3708205
Offset: 0

Views

Author

Robert G. Wilson v, Apr 12 2007

Keywords

Comments

For the same sequence but for base 10 (A070177): 1,6,43,143,471,1511,4959,15914,49580,158148,501883,1582908,5014367,....

Examples

			a(9) = 120 since P(2^9) = 4453575699570940947378 and 4+4+5+3+5+7+5+6+9+9+5+7+0+9+4+0+9+4+7+3+7+8 = 120.

Crossrefs

Cf. A000041, A000079, A007953, A068413, A129490.

Programs

  • Mathematica
    f[n_] := Plus @@ IntegerDigits @PartitionsP[2^n]; Table[ f@n, {n, 0, 42}]

Formula

a(n) = A007953(A000041(A000079(n))) = A007953(A068413(n)).
a(n) =~ 9*A129490(n)/2.

Extensions

Offset corrected by Alois P. Heinz, Sep 20 2024

A347654 Number of partitions of 10^n into distinct odd parts.

Original entry on oeis.org

1, 2, 2574, 517035762467311, 11296895312655297284351876487257601933458562000884410
Offset: 0

Views

Author

Seiichi Manyama, Sep 10 2021

Keywords

Comments

The next term a(5) = 5.5425352720...*10^171 is too large to include.

Links

Crossrefs

Row 10 of A347630.
Cf. A000700, A011557, A069878, A070177, A347626.

Programs

  • PARI
    a(n) = polcoef(prod(k=0, 10^n\2, 1+x^(2*k+1)+x*O(x^(10^n))), 10^n);

Formula

a(n) = A000700(10^n).

A185041 a(n) = number of partitions of 10^n mod 10.

Original entry on oeis.org

1, 2, 2, 1, 4, 9, 8, 0, 2, 9, 9, 5, 6, 5, 7, 2, 1, 6, 9, 6
Offset: 0

Views

Author

Fredrik Johansson, Jan 23 2012

Keywords

Comments

p(10^n) mod 10 where p(n) = A000041(n)

Examples

			p(10^2) = 190569292, so a(2) = 2

Crossrefs

Equals A070177(n) mod 10

Programs

  • Mathematica
    Table[Mod[PartitionsP[10^n], 10], {n, 0, 6}]
  • PARI
    a(n)=numbpart(10^n)%10 \\ Charles R Greathouse IV, Apr 06 2016
Previous Showing 11-13 of 13 results.

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

Content is available under The OEIS End-User License Agreement.