A179790 - OEIS

%I #11 Sep 08 2023 22:42:03

%S 28,83,1516,3420,5503,30889,75228,776563,2428283,3035356,29901479,

%T 68334642,113284785,776887258,1719856432,3353407292,19232010711,

%U 27678166236,29160146546,305337557432,95950163566107,114852386371373

%N Records for minima of the positive distance d between the ninth power of a positive integer x and the square of an integer y such that d = x^9 - y^2 (x <> k^2 and y <> k^9).

%C Distance d is equal to 0 when x = k^2 and y = k^9.

%C For x values see A179791.

%C For y values see A179792.

%C Conjecture (_Artur Jasinski_): For any positive number x >= A179791(n), the distance d between the ninth power of x and the square of any y (such that x <> k^2 and y <> k^9) can't be less than A179790(n).

%t d = 9; 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.

%K nonn

%O 1,1

%A _Artur Jasinski_, Jul 27 2010