A318439 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let h(n) = Sum_{k=0..w} b_k * (i-1)^k (where i denotes the imaginary unit); a(n) is the imaginary part of h(n).

0, 0, 1, 1, -2, -2, -1, -1, 2, 2, 3, 3, 0, 0, 1, 1, 0, 0, 1, 1, -2, -2, -1, -1, 2, 2, 3, 3, 0, 0, 1, 1, -4, -4, -3, -3, -6, -6, -5, -5, -2, -2, -1, -1, -4, -4, -3, -3, -4, -4, -3, -3, -6, -6, -5, -5, -2, -2, -1, -1, -4, -4, -3, -3, 8, 8, 9, 9, 6, 6, 7, 7, 10

Offset: 0

Author

Rémy Sigrist, Aug 26 2018

Keywords

• sign
• look
• base

Comments

See A318438 for the real part of h and additional comments.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A108520, A318438.

Programs

PARI

a(n) = my (d=Vecrev(digits(n,2))); imag(sum(i=1, #d, d[i]*(I-1)^(i-1)))

Formula

a(2^k) = A108520(k-1) for any k > 0.