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A155178 Numbers p of primitive Pythagorean triangles such that perimeters and products of 3 sides 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, pr=a*b*c, pr-+1 are primes.

%I A155178 #2 Mar 31 2012 12:38:20
%S A155178 1,7916,35882,37816,47491,128429,131830,146471,154799,157579,170219,
%T A155178 174964,187544,207829,208039,222887,223142,262502,291544,319825,
%U A155178 327602,331627,353857,476681,477659,494207,522025,537454,540682,558161,571670
%N A155178 Numbers p of primitive Pythagorean triangles such that perimeters and products of 3 sides 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, pr=a*b*c, pr-+1 are primes.
%C A155178 p=1,q=2,a=3,b=4,c=5,s=12-+1 primes,pr=3*4*5=60-+1 primes, ...
%t A155178 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;pr=a*b*c;If[PrimeQ[s-1]&&PrimeQ[s+1]&&PrimeQ[pr-1]&&PrimeQ[pr+1],AppendTo[lst,n]],{n,3*9!}];lst
%Y A155178 Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177
%K A155178 nonn
%O A155178 1,2
%A A155178 _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009