cp's OEIS Frontend

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.

%I A348911 #14 Nov 09 2021 15:01:46
%S A348911 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,
%T A348911 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,
%U A348911 -6,-5,-7,-2,-2,-1,-3,0,0,1,-1,0,0,1,-1,-2,-2,-1,-3
%N 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.
%C A348911 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 A348911 The function f defines a bijection from the nonnegative integers to the Eisenstein integers.
%H A348911 Rémy Sigrist, <a href="/A348911/b348911.txt">Table of n, a(n) for n = 0..16383</a>
%H A348911 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 A348911 Rémy Sigrist, <a href="/A348911/a348911.gp.txt">PARI program for A348911</a>
%H A348911 Gary Teachout, <a href="http://teachout1.net/village/fill2.html">Fractal Space Filling Curves 2002</a>
%H A348911 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_integer">Eisenstein integer</a>
%F A348911 a(2^(k+1)) = A077966(k) for any k >= 0.
%o A348911 (PARI) See Links section.
%Y A348911 See A334493 for a similar sequence.
%Y A348911 Cf. A077966, A348910.
%K A348911 sign,base
%O A348911 0,9
%A A348911 _Rémy Sigrist_, Nov 03 2021