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

0,5

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

Formula

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

Prog

(PARI) See Links section.

Crossrefs

See A334492 for a similar sequence.

Cf. A077966, A348911.

Sequence in context: A129391 A129390 A345255 * A123590 A092872 A364880

Adjacent sequences: A348907 A348908 A348909 * A348911 A348912 A348913

Keyword

sign,base

Author

Rémy Sigrist, Nov 03 2021

Status

approved