cp's OEIS Frontend

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.

%I A348910 #19 Nov 09 2021 15:01:37
%S A348910 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,
%T A348910 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,
%U A348910 -3,-4,-5,-2,-1,-2,-3,-8,-7,-8,-9,-10,-9,-10,-11,-8
%N 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.
%C A348910 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.
%C A348910 The function f defines a bijection from the nonnegative integers to the Eisenstein integers.
%H A348910 Rémy Sigrist, <a href="/A348910/b348910.txt">Table of n, a(n) for n = 0..16383</a>
%H A348910 Rémy Sigrist, <a href="/A348910/a348910.png">Colored representation of f(n) for n = 0..4^10-1 in a hexagonal lattice</a> (where the hue is function of n)
%H A348910 Rémy Sigrist, <a href="/A348910/a348910.gp.txt">PARI program for A348910</a>
%H A348910 Gary Teachout, <a href="http://teachout1.net/village/fill2.html">Fractal Space Filling Curves 2002</a>, section "A Four Tile Star"
%H A348910 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_integer">Eisenstein integer</a>
%F A348910 a(2^k) = A077966(k) for any k >= 0.
%o A348910 (PARI) See Links section.
%Y A348910 See A334492 for a similar sequence.
%Y A348910 Cf. A077966, A348911.
%K A348910 sign,base
%O A348910 0,5
%A A348910 _Rémy Sigrist_, Nov 03 2021