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.

A106505 Ordered and uniqued length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.

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%I A106505 #21 Apr 23 2021 05:42:11
%S A106505 5,7,9,11,13,15,16,17,19,21,23,24,25,27,29,31,32,33,35,37,39,40,41,43,
%T A106505 45,47,48,49,51,53,55,56,57,59,61,63,64,65,67,69,71,72,73,75,77,79,80,
%U A106505 81,83,85,87,88,89,91,93,95,96,97,99,101,103,104,105,107,109,111,112
%N A106505 Ordered and uniqued length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.
%C A106505 The terms are proposed without repetition. For example, there exist two such triangles with a length of side = 33. They correspond respectively to s^2 - r^2 = 33 (see formula) with (r, s) = (4, 7) and sides (33, 28, 16), and the other triangle with (r, s) = (16, 17) and sides (33, 272, 256). Lengths = 39, 51, 57, 69, 75, ... correspond to two distinct triangles ... The lengths of these sides are proposed with repetition in A343064. - _Bernard Schott_, Apr 22 2021
%F A106505 Values s^2 - r^2, where r<s<2r and (r, s)=1.
%F A106505 Conjecture: for n>2, a(n+5) = a(n) + 8. - _Ralf Stephan_, Nov 16 2010.
%F A106505 Empirical g.f.: -x*(x^7+x^6+3*x^5-2*x^4-2*x^3-2*x^2-2*x-5) / ((x-1)^2*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Oct 05 2013
%Y A106505 Cf. A106499-A106506, A106410, A106420, A106430, A321499.
%Y A106505 Cf. A343063, A343064, A343065, A343066, A343067.
%K A106505 nonn
%O A106505 1,1
%A A106505 _Lekraj Beedassy_, May 04 2005
%E A106505 Extended by _Ray Chandler_, May 09 2005