A179798 - OEIS

%I #5 Sep 08 2023 22:39:28

%S 92,1679,39281,89927,296863,1530322,12056004,55972895,67903894,

%T 102383343,641211875,5148097536,13764973788,19839459725,87957606400,

%U 113794567580,126889914716,146745583311,880304597278,1154049177924

%N Record minima of the positive distance d between the 11th 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 x values see A179799.

%C For x values see A179800.

%C Conjecture (_Artur Jasinski_):

%C For any positive number x >= A179799(n), the distance d between the eleventh 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}]; dd

%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