A179814 Values y for 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).

181, 3787, 174692, 685700, 2178889, 5931641, 31622776, 64631634, 1691869691, 2597429617, 16328969210, 22469029417, 54353589638, 380636413501, 2506650894908, 11290681881873, 12924394402851, 127673846293724

Offset

1,1

Comments

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

For d values see A179812.

For x values see A179813.

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..18.

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}]; yy

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: A200953 A264337 A155018 * A293655 A008379 A262141

Adjacent sequences: A179811 A179812 A179813 * A179815 A179816 A179817

Keyword

nonn

Author

Artur Jasinski, Jul 28 2010

Status

approved