A318479 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 square of the modulus of h(n).

0, 1, 2, 1, 4, 5, 2, 1, 8, 13, 10, 13, 4, 9, 2, 5, 16, 9, 26, 17, 20, 13, 26, 17, 8, 5, 18, 13, 4, 1, 10, 5, 32, 41, 18, 25, 52, 61, 34, 41, 40, 53, 26, 37, 52, 65, 34, 45, 16, 17, 10, 9, 36, 37, 26, 25, 8, 13, 2, 5, 20, 25, 10, 13, 64, 65, 82, 81, 36, 37, 50

Offset: 0

Author

Rémy Sigrist, Aug 27 2018

Keywords

• nonn
• 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. A318438, A318439.

Programs

PARI

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

Formula

a(n) = A318438(n)^2 + A318439(n)^2.

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

a(3 * 2^k) = 2^k for any l >= 0.