A330714 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^k (where i denotes the imaginary unit); a(n) is the square of the modulus of h(n).

0, 1, 1, 2, 1, 0, 2, 1, 1, 2, 0, 1, 2, 1, 1, 0, 1, 4, 2, 5, 0, 1, 1, 2, 2, 5, 1, 4, 1, 2, 0, 1, 1, 2, 4, 5, 2, 1, 5, 4, 0, 1, 1, 2, 1, 0, 2, 1, 2, 5, 5, 8, 1, 2, 4, 5, 1, 4, 2, 5, 0, 1, 1, 2, 1, 0, 2, 1, 4, 1, 5, 2, 2, 1, 1, 0, 5, 2, 4, 1, 0, 1, 1, 2, 1

Offset: 0

Author

Seiichi Manyama, Dec 27 2019

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A007088, A131851, A131852, A131853, A131856, A131858, A131860, A290886, A318479.

Programs

Mathematica

a[0] = 0; a[n_] := a[n] = a[Floor[n/2]]*I + Mod[n, 2]; Table[Abs[a[n]]^2, {n, 0, 100}] (* Amiram Eldar, May 06 2021, after Jean-François Alcover at A131851 *)

PARI

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

Formula

a(n) = A131851(n)^2 + A131852(n)^2.