cp's OEIS Frontend

A179107 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.

%I A179107 #34 Oct 30 2017 12:02:05
%S A179107 1,8,15,17,24,225,1090,8569,11492,14668,14857,28024,117073
%N A179107 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.
%C A179107 If x=n^2 and y=n^3 distance d=0.
%C A179107 For x values see A179108.
%C A179107 For y values see A179109.
%C A179107 For numbers x from 46 to 108 distance can't be less than 8.
%C A179107 For numbers x from 109 to 5233 distance can't be less than 15.
%C A179107 For numbers x from 5234 to 8157 distance can't be less than 17.
%C A179107 For numbers x from 8158 to 729113 distance can't be less than 24.
%C A179107 For numbers x from 729114 to 28187350 distance can't be less than 225.
%C A179107 Next conjectured terms are: 4401169, 87002345, 193234265, 497218657.
%H A179107 J. Calvo, J. Herranz, G. Saez, <a href="https://doi.org/10.1090/S0025-5718-09-02240-6">A new algorithm to search for small nonzero |x^3 - y^2| values</a>, Math. Comp. 78 (2009), 2435-2444.
%H A179107 N. Elkies, <a href="http://www.math.harvard.edu/~elkies/hall.html">Hall conjecture</a>
%t A179107 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}]; dd (* _Artur Jasinski_, Oct 30 2011 *)
%Y A179107 Cf. A179108, A179109, A179386, A179387, A179388.
%K A179107 more,nonn
%O A179107 1,2
%A A179107 _Artur Jasinski_, Jun 29 2010