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

Author

Reinhard Zumkeller, Nov 03 2009

Keywords

• nonn

Links

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

Crossrefs

Cf. A167393.

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

Programs

Haskell

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

Mathematica

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 *)

PARI

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

Formula

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