A115378 - OEIS

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

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OFFSET

1,4

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

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

MAPLE

f:= proc(n) 2^numboccur(0, convert(n, base, 2))-1 end proc:

map(f, [$1..100]); # Robert Israel, Feb 16 2026