A070066 Values of y 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.)

3, 9, 16, 16, 32, 48, 24, 6, 55, 72, 72, 100, 72, 112, 72, 108, 144, 162, 36, 192, 72, 100, 216, 72, 295, 343, 351, 359, 72, 368, 423, 343, 216, 300, 343, 648, 800, 783, 625, 833, 400, 450, 648, 972, 496, 576, 1024, 864, 675, 972, 1215, 242, 72, 500, 1176

Offset

1,1

Links

Table of n, a(n) for n=1..55.

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

x-values are in A070065, z-values are in A070067.

Sequence in context: A076362 A336970 A366051 * A299636 A271491 A359618

Adjacent sequences: A070063 A070064 A070065 * A070067 A070068 A070069

Keyword

nonn

Author

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

Status

approved