This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A301626 #23 Mar 27 2018 18:33:29 %S A301626 0,0,0,1,1,1,4,1,1,4,8,2,0,2,8,9,5,1,1,5,9,4,10,4,2,4,10,4,1,5,9,5,5, %T A301626 9,5,1,0,2,8,10,8,10,8,2,0,1,1,5,13,13,13,13,5,1,1,4,2,4,10,20,18,20, %U A301626 10,4,2,4,4,2,4,9,17,25,25,17,9,4,2,4,5,1,1 %N A301626 Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0: T(n, k) = square of the distance from n + k*i to nearest cube of a Gaussian integer (where i denotes the root of -1 with positive imaginary part). %C A301626 The distance between two Gaussian integers is not necessarily integer, hence the use of the square of the distance. %C A301626 This sequence is a complex variant of A074989. %C A301626 See A301636 for the square array dealing with squares of Gaussian integers. %H A301626 Rémy Sigrist, <a href="/A301626/b301626.txt">Table of n, a(n) for n = 0..20300</a> %H A301626 Rémy Sigrist, <a href="/A301626/a301626.png">Colored scatterplot for abs(x) <= 500 and abs(y) <= 500</a> (where the hue is function of sqrt(T(abs(x), abs(y)))) %H A301626 Rémy Sigrist, <a href="/A301626/a301626_1.png">Voronoi diagram of the cubes of Gaussian integers for abs(x) <= 500 and abs(y) <= 500</a> %H A301626 Rémy Sigrist, <a href="/A301626/a301626_2.png">Scatterplot of (x, y) such that T(abs(x), abs(y)) is a square and abs(x) <= 500 and abs(y) <= 500</a> %H A301626 Rémy Sigrist, <a href="/A301626/a301626.gp.txt">PARI program for A301626</a> %H A301626 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gaussian_integer">Gaussian integer</a> %H A301626 Wikipedia, <a href="https://en.wikipedia.org/wiki/Voronoi_diagram">Voronoi diagram</a> %H A301626 <a href="/index/Di#distance_to_the_nearest">Index entries for sequences related to distance to nearest element of some set</a> %F A301626 T(n, k) = T(k, n). %F A301626 T(n, 0) <= A074989(n)^2. %F A301626 T(n, 0) = 0 iff n is a cube (A000578). %F A301626 T(n, k) = 0 iff n + k*i = z^3 for some Gaussian integer z. %e A301626 Square array begins: %e A301626 n\k| 0 1 2 3 4 5 6 7 8 9 10 %e A301626 ---+------------------------------------------------------- %e A301626 0| 0 0 1 4 8 9 4 1 0 1 4 --> A301639 %e A301626 1| 0 1 1 2 5 10 5 2 1 2 2 %e A301626 2| 1 1 0 1 4 9 8 5 4 4 1 %e A301626 3| 4 2 1 2 5 10 13 10 9 5 2 %e A301626 4| 8 5 4 5 8 13 20 17 13 8 5 %e A301626 5| 9 10 9 10 13 18 25 25 18 13 10 %e A301626 6| 4 5 8 13 20 25 32 32 25 20 17 %e A301626 7| 1 2 5 10 17 25 32 41 34 29 26 %e A301626 8| 0 1 4 9 13 18 25 34 45 40 37 %e A301626 9| 1 2 4 5 8 13 20 29 40 53 50 %e A301626 10| 4 2 1 2 5 10 17 26 37 50 65 %o A301626 (PARI) See Links section. %Y A301626 Cf. A000578, A074989, A301636, A301639 (first row/column). %K A301626 nonn,tabl,look %O A301626 0,7 %A A301626 _Rémy Sigrist_, Mar 24 2018