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 A165261 #8 Mar 31 2012 12:38:26
%S A165261 4,12,77,112,143,195,209,220,299,420,425,520,527,629,700,840,868,988,
%T A165261 1023,1085,1127,1209,1305,1421,1480,1720,1740,1900,2001,2021,2255,
%U A165261 2296,2320,2331,2332,2499,2520,2548,2583,2604,2752,2829,2964,3021,3256,3311
%N A165261 Long legs of primitive Pythagorean triples which have a perimeter which is the average of a twin prime pair.
%e A165261 see A165250.
%t A165261 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 A165261 Cf. A020883, A014574, A165260, A165262.
%K A165261 nonn
%O A165261 1,1
%A A165261 _Vladimir Joseph Stephan Orlovsky_, Sep 11 2009