A198832 Values x for records of maxima of positive distance d between a cube of positive integer x and a square of integer y and such that d = x^3 - y^2.

1, 2, 6, 8, 10, 12, 13, 19, 26, 31, 33, 39, 40, 43, 46, 52, 68, 72, 78, 84, 90, 93, 95, 105, 109, 133, 139, 149, 152, 162, 176, 180, 190, 202, 211, 219, 231, 243, 265, 269, 272, 306, 330, 336, 341, 346, 351, 356, 366, 393, 407, 422, 436, 446, 450, 467, 501

Offset: 1

Author

Artur Jasinski, Oct 30 2011

Keywords

• nonn

Links

• J. Calvo, J. Herranz, G. Saez, A new algorithm to search for small nonzero |x^3 - y^2| values, Math. Comp. 78 (2009), 2435-2444.

Crossrefs

Cf. A078933, A179107, A179108, A179109.

Programs

Mathematica

aa = {}; bb = {}; max = -1; Do[kk = x^3 - Floor[x^(3/2)]^2; If[kk > max, AppendTo[aa, kk]; AppendTo[bb, x]; max = kk], {x, 1, 10000}]; bb

Extensions

Definition modified by Harvey P. Dale, Sep 25 2019