A179812 Record minima of the positive distance d between the fifteenth power of a positive integer x and the square of an integer y such that d = x^15 - y^2 (x <> k^2 and y <> k^15).

7, 7538, 283261, 494576, 4235622, 7135951, 38053824, 55905695, 185380312, 1208691743, 3263221507, 14034746735, 14732727599, 24211719874, 68491624661, 136264246246, 5337970328375, 6845918569200, 15505738619231, 30037885135088

Offset

1,1

Comments

Distance d is equal to 0 when x = k^2 and y = k^15.

For x values see A179813.

For y values see A179814.

Conjecture: For any positive number x >= A179813(n), the distance d between the fifteenth power of x and the square of any y (such that x <> k^2 and y <> k^15) can't be less than A179812(n).

Links

Table of n, a(n) for n=1..20.

Mathematica

d = 15; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; dd

Crossrefs

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795, A179798, A179799, A179800, A179812, A179813, A179814.

Sequence in context: A220879 A119528 A116266 * A023344 A297050 A137693

Adjacent sequences: A179809 A179810 A179811 * A179813 A179814 A179815

Keyword

nonn

Author

Artur Jasinski, Jul 28 2010

Status

approved