A179798 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).

92, 1679, 39281, 89927, 296863, 1530322, 12056004, 55972895, 67903894, 102383343, 641211875, 5148097536, 13764973788, 19839459725, 87957606400, 113794567580, 126889914716, 146745583311, 880304597278, 1154049177924

Offset

1,1

Comments

Distance d is equal to 0 when x = k^2 and y = k^13.

For x values see A179799.

For x values see A179800.

Conjecture (Artur Jasinski):

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).

Links

Table of n, a(n) for n=1..20.

Mathematica

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

Crossrefs

Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795, A179798, A179799, A179800.

Sequence in context: A251934 A064203 A265968 * A232795 A269439 A269623

Adjacent sequences: A179795 A179796 A179797 * A179799 A179800 A179801

Keyword

nonn

Author

Artur Jasinski, Jul 27 2010

Status

approved