%I A155187
%S A155187 2,3,11,71,227,491,683,1103,1187,2591,3923,4271,4931,6737,7193,7703,
%T A155187 8093,8753,8963,9173,9377,10271,13043,13451,13997,15233,15443,15803,
%U A155187 15887,17957,18701,19961,20681,21701,22031,22073,24371,24473,24683
%N A155187 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 A155187 p=1,q=2(prime),a=3,b=4,c=5,s=12-+1 primes, ...
%t A155187 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 A155187 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
%Y A155187 Sequence in context: A066046 A065597 A001052 this_sequence A109132 A008510 
               A042165
%Y A155187 Adjacent sequences: A155184 A155185 A155186 this_sequence A155188 A155189 
               A155190
%K A155187 nonn
%O A155187 1,1
%A A155187 Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009