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

Author

Reinhard Zumkeller, Nov 08 2008

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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

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

Python

def A147612(n): return int((m:=3*n+1).bit_length()>(m-3).bit_length()) if n else 1 # Chai Wah Wu, Apr 18 2025

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