A332252 a(n) is the imaginary part of f(n) defined by f(0) = 0 and f(n+1) = f(n) + i^A000120(n) (where i denotes the imaginary unit). Sequence A332251 gives real parts.

0, 0, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, -1, -2, -2, -2, -3, -4, -4, -5, -5, -5, -4, -3, -3, -3, -4, -4, -5, -6, -6, -6, -7, -8, -8, -9, -9, -9, -8, -8, -9, -10, -10, -11, -11, -11, -10, -11, -11, -11, -10, -10, -9, -8, -8, -7, -7, -7

Offset: 0

Author

Rémy Sigrist, Feb 08 2020

Keywords

• sign
• base

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A000120, A332251 (real parts and additional comments).

Programs

PARI

{ z=0; for (n=0, 67, print1 (imag(z) ", "); z += I^hammingweight(n)) }

Formula

For any k >= 0:

- a(2^(4*k)) = 0,

- a(2^(4*k+1)) = (-4)^k,

- a(2^(4*k+2)) = 2*(-4)^k,

- a(2^(4*k+3)) = 2*(-4)^k.