|
%I #9 Sep 08 2023 22:39:24
%S 90,1262,34938,114283,741455,5875603,17403307,28172943,709955183,
%T 936209559,10875326100,25905378592,35572991418,55703353220,
%U 110485434560,182204642678,447245502234,984322154617,2160608565081,3477146726351
%N Values y for record minima of the positive distance d between the thirteenth power of a positive integer x and the square of an integer y such that d = x^13 - y^2 (x <> k^2 and y <> k^13).
%C Distance d is equal to 0 when x = k^2 and y = k^13.
%C For d values see A179798.
%C For x values see A179799.
%C Conjecture: For any positive number x >= A179799(n), the distance d between the 13th power of x and the square of any y (such that x <> k^2 and y <> k^13) can't be less than A179798(n).
%t d = 13; 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
%Y Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795, A179798, A179799, A179800.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jul 27 2010
|
