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%I #2 Mar 31 2012 12:38:20
%S 3,15833,71765,75633,94983,256859,263661,292943,309599,315159,340439,
%T 349929,375089,415659,416079,445775,446285,525005,583089,639651,
%U 655205,663255,707715,953363,955319,988415,1044051,1074909,1081365,1116323
%N Short leg A 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 p=1,q=2,a=3,b=4,c=5,s=12-+1 primes,pr=3*4*5=60-+1 primes, ...
%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;pr=a*b*c;If[PrimeQ[s-1]&&PrimeQ[s+1]&&PrimeQ[pr-1]&&PrimeQ[pr+1],AppendTo[lst,a]],{n,3*9!}];lst
%Y Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009
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