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%I #2 Mar 31 2012 12:38:20
%S 5,13,113,221,841,1741,3961,5101,8581,9941,11705,12013,20605,21841,
%T 23113,26681,47741,61601,78013,82013,102605,103513,122513,151801,
%U 276025,289561,340313,418613,481181,501001,660101,711625,838513,901825,931613
%N Hypotenuse C of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.
%C p=1,q=2,a=3,b=4,c=5,s=12-+1 primes, ...
%t lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],AppendTo[lst,c]],{n,8!}];lst
%Y Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009
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