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 A362496 #9 Apr 24 2023 01:31:49 %S A362496 -1,0,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,2,1,1,0,0,0,0,0,1, %T A362496 1,1,0,0,0,0,0,2,1,1,1,0,0,0,0,0,0,2,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0, %U A362496 0,0,0,0,0,2,1,1,1,1,0,0,0,0,0,0,0,0,2,1,1,1,1 %N A362496 Square array A(n, k), n, k >= 0, read by upwards antidiagonals; if Newton's method applied to the complex function f(z) = z^3 - 1 and starting from n + k*i reaches or converges to exp(2*r*i*Pi/3) for some r in 0..2, then A(n, k) = r, otherwise A(n, k) = -1 (where i denotes the imaginary unit). %C A362496 This sequence is related to the Newton fractal, and exhibits similar rich patterns (see illustration in Links section). %H A362496 Rémy Sigrist, <a href="/A362496/a362496.png">Colored representation of the square array for n, k <= 1000</a> (black, white, blue and red pixels denote, respectively, -1, 0, 1 and 2) %H A362496 Rémy Sigrist, <a href="/A362496/a362496.gp.txt">PARI program</a> %H A362496 Wikipedia, <a href="https://en.wikipedia.org/wiki/Newton_fractal">Newton fractal</a> %H A362496 Wikipedia, <a href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton's method</a> %e A362496 Array A(n, k) begins: %e A362496 n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 %e A362496 ----+------------------------------------------------------ %e A362496 0 | -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 %e A362496 1 | 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 %e A362496 2 | 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1 1 %e A362496 3 | 0 0 0 0 0 2 2 1 1 1 1 1 1 1 1 1 %e A362496 4 | 0 0 0 0 0 0 1 2 2 1 2 1 1 1 1 1 %e A362496 5 | 0 0 0 0 0 0 0 0 2 2 0 1 1 1 1 1 %e A362496 6 | 0 0 0 0 0 0 0 0 2 1 0 2 2 1 2 2 %e A362496 7 | 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 0 %e A362496 8 | 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0 %e A362496 9 | 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 %e A362496 10 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 %e A362496 11 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A362496 12 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A362496 13 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A362496 14 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A362496 15 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %o A362496 (PARI) See Links section. %Y A362496 Cf. A068601. %K A362496 sign,tabl %O A362496 0,26 %A A362496 _Rémy Sigrist_, Apr 22 2023