cp's OEIS Frontend

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.

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).

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%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