A070066 -id:A070066 - cp's OEIS frontend

A070065 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.)

10, 1242, 1024, 5632, 20480, 17920, 37376, 39151, 36599, 15552, 26001, 75000, 124416, 68608, 172800, 209952, 359424, 413343, 579096, 327680, 684288, 1090625, 1306368, 1650240, 1506463, 1529437, 1607445, 1525899, 3637224, 2783744

Offset: 1

Dean Hickerson and Dan Asimov (asimov(AT)msri.org), Apr 18 2002

nonn

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

			The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320) and (20480,32,768).

y-values are in A070066, z-values are in A070067.

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}]]]]

A070067 Values of z in positive integer solutions of x^2 + y^5 = z^3, listed in increasing order of z.

Original entry on oeis.org

7, 117, 128, 320, 768, 832, 1120, 1153, 1226, 1296, 1377, 2500, 2592, 2816, 3168, 3888, 5760, 6561, 6948, 7168, 7776, 10625, 12960, 13968, 16514, 19208, 19926, 20240, 23652, 24384, 29158, 33614, 42768, 60100, 67228, 69984, 70400, 71199

Offset: 1

Dean Hickerson and Dan Asimov (asimov(AT)msri.org), Apr 18 2002

nonn

			The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320) and (20480,32,768).

x-values are in A070065, y-values are in A070066.

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}]]]]

cp's OEIS Frontend

A070065 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.)

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