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%I #14 Jul 27 2017 04:20:33
%S 10,1242,1024,5632,20480,17920,37376,39151,36599,15552,26001,75000,
%T 124416,68608,172800,209952,359424,413343,579096,327680,684288,
%U 1090625,1306368,1650240,1506463,1529437,1607445,1525899,3637224,2783744
%N Values of x in positive integer solutions of x^2 + y^5 = z^3, listed in increasing order of z. (If a z-value occurs twice, list solutions in increasing order of y.)
%C If x is in the sequence, then so is c^15 x for positive integers c, since if (x,y,z) is a solution, so is (c^15 x, c^6 y, c^10 z). - _Robert Israel_, Jul 26 2017
%e The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320) and (20480,32,768).
%t For[z=1, True, z++, z3=z^3; For[y=1, (d=z3-y^5)>0, y++, If[IntegerQ[x=Sqrt[d]], Print[{x, y, z}]]]]
%Y y-values are in A070066, z-values are in A070067.
%K nonn
%O 1,1
%A _Dean Hickerson_ and Dan Asimov (asimov(AT)msri.org), Apr 18 2002