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 A179108 Values x for records of minima of positive distance d between an square cubefree integer y and an cube of positive and squarefree integer x and such d = y^2 - x^3. 31
 2, 46, 109, 5234, 8158, 720114, 28187351, 110781386, 154319269, 384242766, 390620082, 3790689201, 65589428378 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 18 10:39 EDT 2019. Contains 328147 sequences. (Running on oeis4.)