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%I #8 Feb 11 2020 12:13:38
%S 5,13,113,1741,5101,8581,9941,21841,26681,47741,82013,481181,501001,
%T 1009621,2356621,2542513,3279361,3723721,4277813,7757861,8124481,
%U 13204661,25311613,30772013,44170601,48619661,51521401,52541501,54236113,60731221,72902813
%N Primes in A155175.
%C 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 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[c],AppendTo[lst,c]]],{n,8!}];lst (* corrected by _Ray Chandler_, Feb 11 2020 *)
%Y Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009
%E Sequence corrected by _Ray Chandler_, Feb 11 2020
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