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%I #21 Apr 23 2021 05:42:11
%S 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 45,47,48,49,51,53,55,56,57,59,61,63,64,65,67,69,71,72,73,75,77,79,80,
%U 81,83,85,87,88,89,91,93,95,96,97,99,101,103,104,105,107,109,111,112
%N 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 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 Values s^2 - r^2, where r<s<2r and (r, s)=1.
%F Conjecture: for n>2, a(n+5) = a(n) + 8. - _Ralf Stephan_, Nov 16 2010.
%F 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 Cf. A106499-A106506, A106410, A106420, A106430, A321499.
%Y Cf. A343063, A343064, A343065, A343066, A343067.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, May 04 2005
%E Extended by _Ray Chandler_, May 09 2005