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 A336230 Values z of primitive solutions (x, y, z) to the Diophantine equation x^3 + y^3 + 2*z^3 = 128. 0
 1, 4, 9, 25, 49, 81, 121, 169, -224, 225, 289, 361, -383, 441, 504, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2209, -2219, 2401, 2601, -2687, 2809, 3025, 3249, 3481, -3680, 3721, 3969, 4225, -4283, 4417, 4489, 4761, 5041, 5329, -5459 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Terms are arranged in order of increasing absolute value (if equal, the negative number comes first). (5 - 4*n^2)^3 + (5 - 4*(n + 1)^2)^3 + 2*(2*n + 1)^6 = 128. A000290(2*n + 1) are terms of the sequence, i.e., there is an infinity of nontrivial solutions to the equation. REFERENCES R. K. Guy, Unsolved Problems in Number Theory, D5. LINKS EXAMPLE 1^3 + 5^3 + 2 * 1^3 = 128, 1 is a term. (-11)^3 + (-31)^3 + 2 * (25)^3 = 128, 25 is a term. MATHEMATICA Clear[t] t = {}; Do[y = (128 - x^3 - 2 z^3)^(1/3) /. (-1)^(1/3) -> -1; If[IntegerQ[y] && GCD[x, y, z] == 1, AppendTo[t, z]], {z, -4761, 4761}, {x, -11550, 11550}] u = Union@t; v = Table[(-1)^n*Floor[(n + 1)/2], {n, 0, 9523}]; Select[v, MemberQ[u, #] &] CROSSREFS Cf. A000290, A000578, A003215, A004825, A004826, A050791, A130472, A195006. Sequence in context: A332646 A306043 A194269 * A130283 A065739 A053704 Adjacent sequences:  A336227 A336228 A336229 * A336231 A336232 A336233 KEYWORD sign AUTHOR XU Pingya, Jul 12 2020 STATUS approved

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)