This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165236 #3 Mar 31 2012 12:38:26
%S A165236 20,33,44,56,68,273,303,320,380,440,483,740,1071,1089,1101,1220,1376,
%T A165236 1484,1635,1773,1808,1869,1940,1965,2000,2120,2144,2204,2319,2715,
%U A165236 2763,3003,3164,3309,3500,3603,3729,3740,3753,3801,4148,4215,4323,4340,4401
%N A165236 Short legs of primitive Pythagorean Triples (a,b,c) such that 2*a+1, 2*b+1 and 2*c+1 are primes.
%C A165236 Only one instance of a enters the sequence if multiple solutions exist, like with (a,b,c) = (320,999,1049) and (a,b,c) = (320,25599,25601).
%C A165236 Subsequence of A009004. [_R. J. Mathar_, Mar 25 2010]
%e A165236 (a,b,c) = (20,21,29), (33,56,65), (44,483,485), (56,783,785), (68,285,293), (273,4136,4145).
%e A165236 In the first case, for example, 2*20+1=41, 2*21+1 and 2*29+1 are all prime, which adds the half-leg 20 to the sequence.
%t A165236 amax=6*10^4;lst={};k=0;q=12!;Do[If[(e=((n+1)^2-n^2))>amax,Break[]];
%t A165236 Do[If[GCD[m, n]==1,a=m^2-n^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[]];
%t A165236 c=m^2+n^2;If[PrimeQ[2*c+1], k++;AppendTo[lst,a]]]]]];If[a>amax,Break[]],{m,n+1,12!,2}],{n,1,q, 1}];Union@lst
%Y A165236 Cf. A009004, A020883, A165237, A165238
%K A165236 nonn
%O A165236 1,1
%A A165236 _Vladimir Joseph Stephan Orlovsky_, Sep 09 2009
%E A165236 Comments moved to examples and definition clarified by _R. J. Mathar_, Mar 25 2010