A147612 If n is a Jacobsthal number then 1 else 0.

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

Offset

0,1

Comments

a(A001045(n)) = 1; a(A147613(n)) = 0.

Links

Antti Karttunen, Table of n, a(n) for n = 0..43692

Index entries for characteristic functions

Formula

a(n) = 0^(j(n,1)*j(n,-1)) with j(n,i) = if n mod 2 = 0 then n else j((n+i)/2,-i).

a(n) = A105348(n), for n <> 1. - R. J. Mathar, Nov 19 2008

For n > 0, a(n) = A000035(A281228(A265746(n))), where A000035(A281228(n)) is the characteristic function of powers of 3 (A000244). - Antti Karttunen, Oct 09 2017

Mathematica

With[{s = LinearRecurrence[{1, 2}, {0, 1}, 24]}, Array[If[FreeQ[s, #], 0, 1] &, 105, 0]] (* Michael De Vlieger, Oct 09 2017 *)

Prog

(PARI)
A147612aux(n, i) = if(!(n%2), n, A147612aux((n+i)/2, -i));
A147612(n) = 0^(A147612aux(n, 1)*A147612aux(n, -1)); \\ Antti Karttunen, Oct 09 2017

Crossrefs

Cf. A001045, A105348, A265746, A293431, A293432, A293433, A293434.

Sequence in context: A285533 A185175 A322586 * A323509 A197183 A357382

Adjacent sequences: A147609 A147610 A147611 * A147613 A147614 A147615

Keyword

nonn

Author

Reinhard Zumkeller, Nov 08 2008

Status

approved