A179108 Values x for records of minima of positive distance d between a square cubefree integer y and a cube of positive and squarefree integer x and such d = y^2 - x^3.

2, 46, 109, 5234, 8158, 720114, 28187351, 110781386, 154319269, 384242766, 390620082, 3790689201, 65589428378

Offset

1,1

Comments

If x=n^2 and y=n^3 distance d=0.

For d values see A179107.

For y values see A179109.

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.

Next conjectured terms are: 53197086958290, 12813608766102800, 810574762403977000, 471477085999389000.

Links

Table of n, a(n) for n=1..13.

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}]; xx (* Artur Jasinski, Oct 30 2011 *)

Crossrefs

Cf. A179107, A179109.

Cf. A078933. [From R. J. Mathar, Oct 13 2010]

Sequence in context: A090601 A266016 A071777 * A158960 A281327 A302377

Adjacent sequences: A179105 A179106 A179107 * A179109 A179110 A179111

Keyword

more,nonn

Author

Artur Jasinski, Jun 29 2010

Status

approved