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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.
2
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
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.
FORMULA
a(2^(k+1)) = A077966(k) for any k >= 0.
PROG
(PARI) See Links section.
CROSSREFS
See A334493 for a similar sequence.
Sequence in context: A364730 A283004 A111709 * A039996 A039994 A348485
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Nov 03 2021
STATUS
approved