cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A117319 Values of n for which Leech's problem "Find two rational right-angled triangles on the same base whose heights are in the ratio n:1" has a solution.

This page as a plain text file.
%I A117319 #6 Sep 29 2015 17:40:27
%S A117319 7,10,11,12,14,17,19,22,23,27,28,29,30,33,38,39,40,41,42,44,45,47,48,
%T A117319 51,52,53,54,57,58,59,61,67,69,74,76,79,80,81,82,83,84,85,88,92,93,96,
%U A117319 97,100,102,103,105,107,108,109,111,112,113,115,118,119,120,121,124,126
%N A117319 Values of n for which Leech's problem "Find two rational right-angled triangles on the same base whose heights are in the ratio n:1" has a solution.
%C A117319 Integers n such that the elliptic curve y^2  = x^3 + (n^2+1)*x^2 + n^2*x has a positive rank.
%H A117319 Allan MacLeod, <a href="https://web.archive.org/web/20070621053241/http://maths.paisley.ac.uk/allanm/ecrnt/leech/leechint.htm">Solutions to Leech's problem</a>
%e A117319 a(1)=7 because n=7 is the smallest factor n for which both b^2+h^2 and b^2+(n*h)^2 are squares. The corresponding values of base b and height h are b=A117320(1)=12 and h=A117321(1)=5. 12^2+5^2=169=13^2 and 12^2+(7*5)^2=1369=37^2 are both squares.
%o A117319 (PARI) { isA117319(n) = ellanalyticrank(ellinit([0, n^2+1, 0, n^2, 0]))[1]; } /* _Max Alekseyev_, Sep 29 2015 */
%Y A117319 Cf. A117320 (bases), A117321 (heights), A228380.
%K A117319 nonn
%O A117319 1,1
%A A117319 _Hugo Pfoertner_, Mar 07 2006