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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.
2
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, Colored representation of f(n) for n = 0..4^10-1 in a hexagonal lattice (where the hue is function of n)
Gary Teachout, Fractal Space Filling Curves 2002, section "A Four Tile Star"
FORMULA
a(2^k) = A077966(k) for any k >= 0.
PROG
(PARI) See Links section.
CROSSREFS
See A334492 for a similar sequence.
Sequence in context: A129391 A129390 A345255 * A123590 A092872 A364880
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Nov 03 2021
STATUS
approved