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

0,4

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

Formula

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

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

Prog

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

Crossrefs

Cf. A318702.

Sequence in context: A132042 A303977 A060370 * A165064 A299918 A021418

Adjacent sequences: A318701 A318702 A318703 * A318705 A318706 A318707

Keyword

nonn,base,look

Author

Rémy Sigrist, Sep 01 2018

Status

approved