
COMMENTS

If x=n^2 and y=n^3 distance d=0.
For x values see A179108.
For d values see A179107.
For numbers x from 46 to 108 distance can't be less than 8.
For numbers x from 109 to 5233 distance can't be less than 15.
For numbers x from 5234 to 8157 distance can't be less than 17.
For numbers x from 8158 to 729113 distance can't be less than 24.
For numbers x from 729114 to 28187350 distance can't be less than 225.


MATHEMATICA

d = 3; 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)] + 1; k = m^2  n^d; 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, 720114}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; yy (* Artur Jasinski, Oct 30 2011 *)
