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.

A020919 Partition numbers mod 11.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 0, 4, 0, 8, 9, 1, 0, 2, 3, 0, 0, 0, 0, 6, 0, 0, 1, 1, 2, 0, 5, 7, 0, 0, 5, 0, 0, 1, 1, 0, 3, 0, 0, 0, 4, 0, 0, 0, 1, 1, 2, 3, 5, 0, 0, 0, 0, 8, 0, 1, 0, 2, 0, 0, 7, 0, 0, 6, 0, 9, 1, 1, 2, 3, 5, 7, 0, 4, 0, 0, 9, 1, 0, 2, 3, 0, 0, 0, 0, 0, 8, 0, 1, 1, 2, 3, 5, 7, 0, 4, 0, 8, 0, 1, 1, 2, 3, 5, 0
Offset: 0

Views

Author

David W. Wilson

Keywords

Comments

Zeros are uncommonly dense at beginning of sequence, no other modulus exhibits this behavior.

Links

Crossrefs

Cf. A000041, A040051, A068907, A068908, A020919.

Programs

  • Mathematica
    Mod[PartitionsP[Range[0,120]],11] (* Harvey P. Dale, May 14 2023 *)
  • PARI
    a(n) = numbpart(n) % 11; \\ Michel Marcus, Jul 14 2022

Formula

a(n) = A000041(n) mod 11. - Sean A. Irvine, May 04 2019

A068907 Number of partitions of n modulo 3.

Original entry on oeis.org

1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 1, 2, 2, 2, 0, 2, 0, 0, 1, 1, 2, 0, 2, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 0
Offset: 0

Views

Author

Henry Bottomley, Mar 05 2002

Keywords

Comments

Of the partitions of numbers from 1 to 100000: 33344 are 0, 33193 are 1 and 33463 are 2 modulo 3.

Links

Crossrefs

Cf. A040051, A068908, A068909, A020919.

Programs

Formula

a(n) = A010872(A000041(n)) = A068906(3, n)
a(n) = Pm(n,1) with Pm(n,k) = if kReinhard Zumkeller, Jun 09 2009

A068906 Square array read by ascending antidiagonals of partitions of k modulo n.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 1, 1, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 0, 0, 3, 2, 5, 3, 2, 1, 0, 0, 1, 3, 1, 1, 5, 3, 2, 1, 0, 0, 0, 2, 0, 5, 0, 5, 3, 2, 1, 0, 0, 0, 2, 2, 3, 4, 7, 5, 3, 2, 1, 0, 1, 2, 2, 0, 4, 1, 3, 7, 5, 3, 2, 1, 0, 1, 2, 0, 2, 0, 1, 7, 2, 7, 5, 3, 2, 1
Offset: 1

Views

Author

Henry Bottomley, Mar 05 2002

Keywords

Comments

0 is disproportionately common modulo 5, 7 and 11, largely because T(5,5m+4)=T(7,7m+5)=T(11,11m+6)=0.

Examples

			Rows start 0,0,0,0,0,...; 1,0,1,1,1,...; 1,2,0,2,1,...; 1,2,3,1,3,...; 1,2,3,0,2,1,...; 1,2,3,5,1,5,...; 1,2,3,5,0,...; 1,2,3,5,7,...; etc.

Links

Crossrefs

Rows 2, 3, 5, 7 and 11 give A040051, A068907, A068908, A068909, A020919.

Formula

T(n, k) =A051127(n, A000041(k))

A068909 Number of partitions of n modulo 7.

Original entry on oeis.org

1, 1, 2, 3, 5, 0, 4, 1, 1, 2, 0, 0, 0, 3, 2, 1, 0, 3, 0, 0, 4, 1, 1, 2, 0, 5, 0, 0, 1, 1, 4, 3, 5, 0, 4, 1, 1, 0, 3, 0, 0, 0, 2, 2, 2, 3, 5, 0, 0, 2, 1, 4, 0, 0, 0, 0, 3, 2, 2, 3, 5, 0, 4, 2, 2, 2, 3, 5, 0, 4, 3, 2, 4, 6, 5, 0, 0, 2, 2, 4, 3, 5, 0, 0, 3, 3, 6, 6, 3, 0, 1, 3, 3, 4, 3, 5, 0, 0, 4, 3, 4, 6, 5, 0, 1
Offset: 0

Views

Author

Henry Bottomley, Mar 05 2002

Keywords

Comments

Of the partitions of numbers from 1 to 100000: 27193 are 0, 12078 are 1, 12203 are 2, 12260 are 3, 12231 are 4, 12003 are 5 and 12032 are 6 modulo 7, largely because the number of partitions of 7m+5 is always a multiple of 7.

Links

Crossrefs

Cf. A000041, A010876, A068906.
Cf. A040051, A068907, A068908, A020919.

Programs

  • Mathematica
    Table[Mod[PartitionsP[n],7],{n,0,110}] (* Harvey P. Dale, Feb 17 2018 *)
  • PARI
    a(n) = numbpart(n) % 7; \\ Michel Marcus, Jul 14 2022

Formula

a(n) = A010876(A000041(n)) = A068906(7, n).
a(n) = Pm(n,1) with Pm(n,k) = if kReinhard Zumkeller, Jun 09 2009]
Showing 1-4 of 4 results.

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