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 A336449 #14 Oct 06 2021 08:31:18
%S A336449 1,9,16,25,49,81,121,169,225,289,-356,361,441,529,625,729,841,-948,
%T A336449 961,1045,1089,1225,1369,1521,1681,-1715,1849,1876,2025,2209,2401,
%U A336449 2601,2809,3025,3249,3481,-3587,3721,3969,4225,4489,4761,5041,5329,5625,5769,5929
%N A336449 Values z of primitive solutions (x, y, z) to the Diophantine equation x^3 + y^3 + 2*z^3 = 2*4^6.
%C A336449 Terms are arranged in order of increasing absolute value (if equal, the negative number comes first).
%C A336449 Let x = a^(2*k) - (a^k)*t - t^2, y = a^(2*k) + (a^k)*t - t^2, z = t^2; then x^3 + y^3 + 2*z^3 = 2*a^(6*k). When a = 4, k = 1, t = 2*n + 1; (x, y, z) are primitive solutions of equation. Thus, terms of A016754 are terms of the sequence.
%D A336449 R. K. Guy, Unsolved Problems in Number Theory, D5.
%e A336449 (-15)^3 + (-27)^3 + 2*25^3 = 11^3 + (-29)^3 + 2*25^3 = 8192, 25 is a term.
%e A336449 (-65)^3 + (449)^3 + 2*(-356)^3 = 8192, -356 is a term.
%t A336449 Clear[t]
%t A336449 t = {};
%t A336449 Do[y = (8192 - x^3 - 2z^3)^(1/3) /. (-1)^(1/3) -> -1;
%t A336449 If[Abs@x <= Abs@y && IntegerQ[y] && GCD[x, y, z] == 1, AppendTo[t, z]], {z, -5929, 5929}, {x, -Round[(Abs[8192 - 2z^3]/3)^(1/2)], Round[(Abs[8192 - 2z^3]/3)^(1/2)]}]
%t A336449 u = Union@t;
%t A336449 v = Table[(-1)^n*Floor[(n + 1)/2], {n, 0, 12000}];
%t A336449 Select[v, MemberQ[u, #] &]
%Y A336449 Cf. A000290, A000578, A003215, A004825, A004826, A016754, A050791, A130472, A195006, A336450.
%K A336449 sign
%O A336449 1,2
%A A336449 _XU Pingya_, Aug 08 2020