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 1-2 of 2 results.

A072246 Numbers which are simultaneously the number of partitions of some k and the number of distinct partitions of some m.

Original entry on oeis.org

1, 2, 3, 5, 15, 22
Offset: 1

Views

Author

Robert G. Wilson v, Jul 06 2002

Keywords

Comments

No more terms for all A000041(k) and A000009(m), where k<=1002505 and m<=2000000. - Vaclav Kotesovec, May 29 2018

Crossrefs

Intersection of A000041 and A000009; A368036 and A368037.

Programs

  • Mathematica
    Intersection[ Table[ PartitionsP[n], {n, 1, 5000}], Table[ PartitionsQ[n], {n, 1, 7000}]]

Formula

A167392(a(n))*A167393(a(n)) = 1. [From Reinhard Zumkeller, Nov 03 2009]

Extensions

Perhaps there are no more terms? - N. J. A. Sloane Jul 06 2002

A368037 Numbers k such that the number of strict partitions of k is the number of unrestricted partitions of some number.

Original entry on oeis.org

1, 2, 3, 4, 7, 8
Offset: 1

Views

Author

Clark Kimberling, Dec 23 2023

Keywords

Comments

Are there others? See A072246.

Examples

			The 1 partition of 1 is [1]; the 1 strict partition of 1 is [1].
The 2 partitions of 2 are [2] and [1,1]; the 2 strict partitions of 3 are [3] and [2,1].
The 3 partitions of 3 are [3], [2,1], [1,1,1]; the 3 strict partitions of 5 are [5], [4,1], [3,2].
The 5 partitions of 4 are [4], [3,1], [2,2], [2,1,1], [1,1,1,1]; the 5 restricted partitions of 7 are [7], [6,1], [5,2], [4,3], [4,2,1].
		

Crossrefs

Showing 1-2 of 2 results.