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

0,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for characteristic functions

Formula

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

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 *)

Prog

(PARI) a(n) = {k=0; while ((pk=numbpart(k)) != n, if (pk > n, return(0)); k++); return (1); } \\ Michel Marcus, Nov 03 2015
(Haskell)
import Data.List.Ordered (member)
a167392 = fromEnum . flip member a000041_list
-- Reinhard Zumkeller, Nov 03 2015

Crossrefs

Cf. A167393.

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

Sequence in context: A159637 A095076 A285080 * A190201 A189702 A168395

Adjacent sequences: A167389 A167390 A167391 * A167393 A167394 A167395

Keyword

nonn

Author

Reinhard Zumkeller, Nov 03 2009

Status

approved