cp's OEIS Frontend

A179813 Values x 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).

%I A179813 #17 Sep 08 2023 22:39:16
%S A179813 2,3,5,6,7,8,10,11,17,18,23,24,27,35,45,55,56,76,78,84,111,114,115,
%T A179813 117,118,139,164,172,175,176,179,183,188,190,193,305,316,377,395,461,
%U A179813 466,483,485,654,747,868,877,931,1045,1434,1822,2199,2645,2754,3171,3961
%N A179813 Values x 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).
%C A179813 Distance d is equal to 0 when x = k^2 and y = k^15.
%C A179813 For x values see A179813.
%C A179813 For y values see A179814.
%C 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).
%t A179813 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}]; xx
%Y A179813 Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795, A179798, A179799, A179800, A179812, A179813, A179814.
%K A179813 nonn
%O A179813 1,1
%A A179813 _Artur Jasinski_, Jul 28 2010