A348910 a(n) is the "real" 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 A348911 gives "w" parts.

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

Offset: 0

Author

Rémy Sigrist, Nov 03 2021

Keywords

• sign
• base

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 A348910
• Gary Teachout, Fractal Space Filling Curves 2002, section "A Four Tile Star"
• Wikipedia, Eisenstein integer

Crossrefs

See A334492 for a similar sequence.

Cf. A077966, A348911.

Programs

PARI

See Links section.

Formula

a(2^k) = A077966(k) for any k >= 0.