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 A301636 #11 Mar 26 2018 20:04:48 %S A301636 0,0,1,1,1,0,1,2,1,1,0,2,4,2,4,1,1,4,2,4,9,4,2,4,1,1,5,4,4,5,5,2,0,2, %T A301636 5,1,1,5,8,5,1,1,5,2,0,0,2,8,10,4,2,4,5,1,1,1,1,5,10,8,5,5,9,4,2,4,4, %U A301636 2,4,9,5,5,8,10,9,5,5,9,9,5,5,9,4,2,4,10 %N A301636 Square array T(n, k) read by antidiagonals upwards, n >= 0 and k >= 0: T(n, k) = square of the distance from n + k*i to nearest square of a Gaussian integer (where i denotes the root of -1 with positive imaginary part). %C A301636 The distance between two Gaussian integers is not necessarily integer, hence the use of the square of the distance. %C A301636 This sequence is a complex variant of A053188. %C A301636 See A301626 for the square array dealing with cubes of Gaussian integers. %H A301636 Rémy Sigrist, <a href="/A301636/a301636.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 A301636 Rémy Sigrist, <a href="/A301636/a301636_1.png">Voronoi diagram of the squares of Gaussian integers for abs(x) <= 500 and abs(y) <= 500</a> %H A301636 Rémy Sigrist, <a href="/A301636/a301636_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 A301636 Rémy Sigrist, <a href="/A301636/a301636.gp.txt">PARI program for A301636</a> %H A301636 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gaussian_integer">Gaussian integer</a> %H A301636 Wikipedia, <a href="https://en.wikipedia.org/wiki/Voronoi_diagram">Voronoi diagram</a> %H A301636 <a href="/index/Di#distance_to_the_nearest">Index entries for sequences related to distance to nearest element of some set</a> %F A301636 T(n, 0) <= A053188(n)^2. %F A301636 T(n, 0) = 0 iff n is a square (A000290). %F A301636 T(0, k) = 0 iff k is twice a square (A001105). %F A301636 T(n, k) = 0 iff n + k*i = z^2 for some Gaussian integer z. %e A301636 Square array begins: %e A301636 n\k| 0 1 2 3 4 5 6 7 8 9 10 %e A301636 ---+------------------------------------------------------- %e A301636 0| 0 1 0 1 4 9 4 1 0 1 4 %e A301636 1| 0 1 1 2 4 5 5 2 1 2 5 %e A301636 2| 1 2 4 2 1 2 5 5 4 5 8 %e A301636 3| 1 2 4 1 0 1 4 9 9 10 8 %e A301636 4| 0 1 4 2 1 2 5 10 16 10 5 %e A301636 5| 1 2 5 5 4 5 8 10 13 9 4 %e A301636 6| 4 5 8 10 8 5 4 5 8 10 5 %e A301636 7| 4 5 8 10 5 2 1 2 5 10 8 %e A301636 8| 1 2 5 9 4 1 0 1 4 9 13 %e A301636 9| 0 1 4 9 5 2 1 2 5 10 17 %e A301636 10| 1 2 5 10 8 5 4 5 8 13 20 %o A301636 (PARI) See Links section. %Y A301636 Cf. A000290, A001105, A053188, A301626. %K A301636 nonn,tabl %O A301636 0,8 %A A301636 _Rémy Sigrist_, Mar 25 2018