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

0,3

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

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.

Prog

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

Crossrefs

Cf. A318438, A318439.

Sequence in context: A229763 A163509 A161399 * A053985 A091564 A321301

Adjacent sequences: A318476 A318477 A318478 * A318480 A318481 A318482

Keyword

nonn,look,base

Author

Rémy Sigrist, Aug 27 2018

Status

approved