%I A155185
%S A155185 5,13,841,1741,3961,5101,8581,276025,289561,711625,2906461,3545785,
%T A155185 3723721,4533061,5187421,5284501,5947801,11286001,19052965,21773401,
%U A155185 23344945,26129221,37575781,41032741,43459165,45324721,47229481
%N A155185 Primes in A155175.
%C A155185 Hypotenuse C (prime numbers only) 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, ar=a*b/2; s=a+b+c, s-+1 are primes. p=1,q=2,a=3,
               b=4,c=5=prime,s=12-+1primes, ...
%t A155185 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[a],AppendTo[lst,c]]],{n,8!}];lst
%Y A155185 Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, 
               A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, 
               A096891, A066885, A099776, A110494, A081589
%Y A155185 Sequence in context: A012033 A007540 A157250 this_sequence A009157 A153374 
               A012032
%Y A155185 Adjacent sequences: A155182 A155183 A155184 this_sequence A155186 A155187 
               A155188
%K A155185 nonn
%O A155185 1,1
%A A155185 Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 21 2009