A115378 a(n) = number of positive integers k < n such that n XOR k = (n+k).

0, 1, 0, 3, 1, 1, 0, 7, 3, 3, 1, 3, 1, 1, 0, 15, 7, 7, 3, 7, 3, 3, 1, 7, 3, 3, 1, 3, 1, 1, 0, 31, 15, 15, 7, 15, 7, 7, 3, 15, 7, 7, 3, 7, 3, 3, 1, 15, 7, 7, 3, 7, 3, 3, 1, 7, 3, 3, 1, 3, 1, 1, 0, 63, 31, 31, 15, 31, 15, 15, 7, 31, 15, 15, 7, 15, 7, 7, 3, 31, 15, 15, 7, 15, 7, 7, 3, 15, 7, 7, 3, 7, 3

Offset: 1

Author

Paul D. Hanna, Jan 21 2006

Keywords

• nonn

Comments

The number of positive integers k < n such that n XOR k = (n-k) is A038573(n).

Crossrefs

Cf. A080791, A080100, A038573.

Programs

PARI

a(n)=sum(k=1,n,if(bitxor(n,k)==(n+k),1,0))

Formula

a(n) = -1 + 2^(number of 0's in binary expansion of n). a(n) = 2^A080791(n) - 1 = A080100(n) - 1.