cp's OEIS Frontend

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.

%I A155187 #4 Dec 31 2023 17:51:22
%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.
%K A155187 nonn
%O A155187 1,1
%A A155187 _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009