A348911 - OEIS

A348911

a(n) is the "w" part of f(n) = Sum_{k>=0, d_k>0} w^(d_k-1) * (-2)^k where Sum_{k>=0} d_k * 4^k is the base-4 representation of n and w = -1/2 + sqrt(-3)/2 is a primitive cube root of unity; sequence A348910 gives "real" parts.

0, 0, 1, -1, 0, 0, 1, -1, -2, -2, -1, -3, 2, 2, 3, 1, 0, 0, 1, -1, 0, 0, 1, -1, -2, -2, -1, -3, 2, 2, 3, 1, 4, 4, 5, 3, 4, 4, 5, 3, 2, 2, 3, 1, 6, 6, 7, 5, -4, -4, -3, -5, -4, -4, -3, -5, -6, -6, -5, -7, -2, -2, -1, -3, 0, 0, 1, -1, 0, 0, 1, -1, -2, -2, -1, -3

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OFFSET

0,9

COMMENTS

For any Eisenstein integer z = u + v*w (where u and v are integers), we call u the "real" part of z and v the "w" part of z.

The function f defines a bijection from the nonnegative integers to the Eisenstein integers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16383

Rémy Sigrist, Colored representation of f(n) for n = 0..4^10-1 in a hexagonal lattice (where the hue is function of n)

Rémy Sigrist, PARI program for A348911

Gary Teachout, Fractal Space Filling Curves 2002

Wikipedia, Eisenstein integer