%I #9 Mar 31 2012 12:38:26
%S 21,56,285,483,783,999,1269,1593,1911,2613,3003,3596,3621,3740,4136,
%T 4233,4928,5096,5451,5828,5840,6320,7040,7280,8036,8468,9021,9296,
%U 9591,11660,12075,12573,12705,12920,12956,13563,14396,14595,15429,15561
%N Long legs of primitive Pythagorean triples (a,b,c) for which 2a+1, 2b+1 and 2c+1 are primes.
%e See A165236.
%t amax=6*10^4;lst={};k=0;q=12!;Do[If[(e=((n+1)^2n^2))>amax,Break[]];Do[If[GCD[m,n]==1,a=m^2n^2;If[PrimeQ[2*a+1],b=2*m*n;If[PrimeQ[2*b+1],If[GCD[a,b]==1,If[a>b,{a,b}={b,a}];If[a>amax,Break[]];c=m^2+n^2;If[PrimeQ[2*c+1],k++;AppendTo[lst,b]]]]]];If[a>amax,Break[]],{m,n+1,12!,2}],{n,1,q,1}];Union@lst
%Y Cf. A020883, A165236, A156238.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 09 2009
