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%I #3 Mar 31 2012 12:38:26
%S 56,63,77,117,120,143,153,156,171,176,187,220,224,240,247,253,273,304,
%T 323,345,352,357,360,364,377,396,403,416,435,437,456,460,468,475,476,
%U 483,493,513,525,527,528,544,561,621,624,627,644,663,665,667,672,680
%N Long legs in primitive Pythagorean triangles with three side lengths of composite integers.
%C The sequence collects the numbers B such that A^2+B^2=C^2, A<B<C, gcd(A,B,C)=1 and such that all
%C three of A, B and C are in A002808. If there are two or more triangles of this kind with the same B,
%C like (A,B,C) = (1003,1596,1885) and (A,B,C) = (1403,1596,2125), only one instance
%C of B is added to the sequence.
%e (A,B,C)=(33,56,65) contributes B=56 to the sequence. (A,B,C)=(16,63,65) contributes B=63 to the sequence.
%t lst={}; Do[Do[If[IntegerQ[c=Sqrt[a^2+b^2]] && GCD[a,b,c]==1,If[ !PrimeQ[a]&&!PrimeQ[b] && !PrimeQ[c], AppendTo[lst,b]]],{a,b-1,3,-1}], {b,4,2000,1}];Union@lst
%Y Cf. A020882, A020883, A165158, A165160.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 06 2009
%E Edited by _R. J. Mathar_, Oct 02 2009