A341509 a(n) = 2^j if n is of the form 2^i - 2^j with i > j, and 0 otherwise.

0, 1, 2, 1, 4, 0, 2, 1, 8, 0, 0, 0, 4, 0, 2, 1, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 2, 1, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 2, 1, 64, 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, 32, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Antti Karttunen, Feb 13 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005940, A006519, A014963, A156552, A340375.

Cf. A023758 (after its initial zero, gives the positions nonzero terms).

Programs

PARI

A006519(n) = (1<A340375(n) = if(n<5, 1, n>>=valuation(n, 2); n++; n>>valuation(n, 2)==1); \\ After function "is" given in A023758
A341509(n) = if(!n,n,A340375(n)*A006519(n));

Formula

a(0) = 0, and for n >= 1, a(n) = A340375(n) * A006519(n).

a(n) = A156552(A014963(A005940(1+n))).