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%I #8 Mar 31 2012 12:38:26
%S 4,12,77,112,143,195,209,220,299,420,425,520,527,629,700,840,868,988,
%T 1023,1085,1127,1209,1305,1421,1480,1720,1740,1900,2001,2021,2255,
%U 2296,2320,2331,2332,2499,2520,2548,2583,2604,2752,2829,2964,3021,3256,3311
%N Long legs of primitive Pythagorean triples which have a perimeter which is the average of a twin prime pair.
%e see A165250.
%t amax=10^5;lst={};k=0;q=12!;Do[If[(e=((n+1)^2-n^2))>amax,Break[]];Do[If[GCD[m,n]==1,a=m^2-n^2;b=2*m*n;If[GCD[a,b]==1,If[a>b,{a,b}={b,a}];If[a>amax,Break[]];c=m^2+n^2;x=a+b+c;If[PrimeQ[x-1]&&PrimeQ[x+1],k++;AppendTo[lst,b]]]],{m,n+1,12!,2}],{n,1,q,1}];Union@lst
%Y Cf. A020883, A014574, A165260, A165262.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 11 2009
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