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 A334493 a(n) is the "w" part of f(n) = Sum_{k>=0, d_k>0} (1+w)^(d_k-1) * (3+w)^k where Sum_{k>=0} d_k * 7^k is the base 7 representation of n and w = -1/2 + sqrt(-3)/2 is a primitive cube root of unity; sequence A334492 gives "real" parts. 7
 0, 0, 1, 1, 0, -1, -1, 1, 1, 2, 2, 1, 0, 0, 3, 3, 4, 4, 3, 2, 2, 2, 2, 3, 3, 2, 1, 1, -1, -1, 0, 0, -1, -2, -2, -3, -3, -2, -2, -3, -4, -4, -2, -2, -1, -1, -2, -3, -3, 5, 5, 6, 6, 5, 4, 4, 6, 6, 7, 7, 6, 5, 5, 8, 8, 9, 9, 8, 7, 7, 7, 7, 8, 8, 7, 6, 6, 4, 4, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 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. This sequence has connections with A316658; here we work with Eisenstein integers, there with Gaussian integers. It appears that f defines a bijection from the nonnegative integers to the Eisenstein integers. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..16806 Rémy Sigrist, PARI program for A334493 Wikipedia, Eisenstein integer EXAMPLE The following diagram depicts f(n) for n = 0..13: "w" axis \ . . . . . . . . \ 10 9 \ . . . . . . . . 3 \ 2 11 7 8 \ ._____._____._____._____._____._____._____. "real" axis 4 0 \ 1 12 13 \ . . . . . . . . 5 6 \ - f(9) = 4 + 2*w, hence a(9) = 2. PROG (PARI) See Links section. CROSSREFS Cf. A307012 (equivalent coordinate for a counterclockwise spiral), A316658, A334492. Sequence in context: A122865 A246656 A352988 * A074080 A359440 A347687 Adjacent sequences: A334490 A334491 A334492 * A334494 A334495 A334496 KEYWORD sign,base,look AUTHOR Rémy Sigrist, May 03 2020 STATUS approved

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Last modified February 21 09:51 EST 2024. Contains 370228 sequences. (Running on oeis4.)