A318704 For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the square of the modulus of f(n).

0, 1, 1, 2, 4, 1, 5, 2, 4, 5, 1, 2, 8, 5, 5, 2, 16, 25, 17, 26, 4, 9, 5, 10, 20, 29, 17, 26, 8, 13, 5, 10, 16, 17, 25, 26, 20, 17, 29, 26, 4, 5, 9, 10, 8, 5, 13, 10, 32, 41, 41, 50, 20, 25, 29, 34, 20, 29, 25, 34, 8, 13, 13, 18, 64, 49, 65, 50, 100, 81, 101

Offset: 0

Author

Rémy Sigrist, Sep 01 2018

Keywords

• nonn
• base
• look

Comments

See A318702 for the real part of f and additional comments.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A318702.

Programs

PARI

a(n) = my (b=Vecrev(binary(n))); norm(sum(k=1, #b, b[k] * I^(k-1) * 2^floor((k-1)/2)))

Formula

a(n) = A318702(n)^2 + A318703(n)^2.

a(4 * k) = 4 * a(k) for any k >= 0.