A167393 -id:A167393 - cp's OEIS frontend

A167392 Characteristic function of partition numbers.

0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset: 0

Reinhard Zumkeller, Nov 03 2009

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for characteristic functions

Cf. A167393.

For n >= 1, column 1 of A186114, also right border of A193870. - Omar E. Pol, Aug 14 2011

import Data.List.Ordered (member)
a167392 = fromEnum . flip member a000041_list
-- Reinhard Zumkeller, Nov 03 2015

nmax = 14;
(* nmax=14 gives P(nmax)+1 = 136 terms; nmax=33 gives 10144 terms *)
PP = Table[PartitionsP[n], {n, 0, nmax}];
a[n_] := Boole[MemberQ[PP, n]];
Table[a[n], {n, 0, PartitionsP[nmax]}] (* Jean-François Alcover, Mar 02 2019 *)

a(n) = {k=0; while ((pk=numbpart(k)) != n, if (pk > n, return(0)); k++); return (1);} \\ Michel Marcus, Nov 03 2015

a(A000041(n)) = 1; a(A167376(n)) = 0.

A167377 Complement of the range of A000009.

Original entry on oeis.org

0, 7, 9, 11, 13, 14, 16, 17, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88

Offset: 1

Reinhard Zumkeller, Nov 03 2009

nonn

A167393(a(n)) = 0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000009, A167376.

import Data.List.Ordered (minus)
a167377 n = a167377_list !! n
a167377_list = minus [0..] a000009_list
-- Reinhard Zumkeller, Nov 03 2015

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

Robert G. Wilson v, Jul 06 2002

nonn

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

Intersection of A000041 and A000009; A368036 and A368037.

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

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

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

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A167392 Characteristic function of partition numbers.

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A167377 Complement of the range of A000009.

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

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