A070065 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

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

MATHEMATICA

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}]]]]

CROSSREFS

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

Sequence in context: A194497 A287226 A015108 * A222793 A320959 A013367

Adjacent sequences: A070062 A070063 A070064 * A070066 A070067 A070068

KEYWORD

nonn

AUTHOR

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

STATUS

approved