cp's OEIS Frontend

A179175 a(n) = least positive k such that Mordell's equation y^2 = x^3 - k has exactly n integral solutions.

%I A179175 #24 Aug 04 2024 20:48:41
%S A179175 3,1,2,1331,4,216,28,54872,116,343,828,250047,496,71991296,207
%N A179175 a(n) = least positive k such that Mordell's equation y^2 = x^3 - k has exactly n integral solutions.
%C A179175 The status of further terms is:
%C A179175   15 integral solutions: unknown
%C A179175   16 integral solutions: 503
%C A179175   17 integral solutions: unknown
%C A179175   18 integral solutions: 431
%C A179175   19 integral solutions: unknown
%C A179175   20 integral solutions: 2351
%C A179175   21 integral solutions: unknown
%C A179175   22 integral solutions: 3807
%C A179175 For least positive k such that equation y^2 = x^3 + k has exactly n integral solutions, see A179162.
%C A179175 If n is odd, then a(n) is perfect cube. [Ray Chandler]
%C A179175 From _Jose Aranda_, Aug 04 2024: (Start)
%C A179175 About those unknown terms:
%C A179175 a(15) <=    2600^3 = (26* 10^2)^3
%C A179175 a(17) <=   10400^3 = (26* 20^2)^3
%C A179175 a(19) <=   93600^3 = (26* 60^2)^3
%C A179175 a(21) <= 4586400^3 = (26*420^2)^3
%C A179175 The term a(13) = 71991296 = 416^3 = (26*4^2)^3. (End)
%H A179175 J. Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a> [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
%Y A179175 Cf. A081120, A081121, A179163-A179174.
%K A179175 nonn,hard,more
%O A179175 0,1
%A A179175 _Artur Jasinski_, Jun 30 2010
%E A179175 Edited and a(7), a(11), a(13) added by _Ray Chandler_, Jul 11 2010