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

0,4

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to coordinates of 2D curves

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).

Prog

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

Crossrefs

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

Sequence in context: A059253 A108133 A341120 * A238268 A194883 A328404

Adjacent sequences: A332249 A332250 A332251 * A332253 A332254 A332255

Keyword

sign,base

Author

Rémy Sigrist, Feb 08 2020

Status

approved