

A167392


Characteristic function of partition numbers.


12



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
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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]}] (* JeanFrançois 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



