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%I #4 Dec 31 2023 17:51:22
%S 2,3,11,71,227,491,683,1103,1187,2591,3923,4271,4931,6737,7193,7703,
%T 8093,8753,8963,9173,9377,10271,13043,13451,13997,15233,15443,15803,
%U 15887,17957,18701,19961,20681,21701,22031,22073,24371,24473,24683
%N Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.
%C p=1, q=2(prime), 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;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[q],AppendTo[lst,q]]],{n,8!}];lst
%Y Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009
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