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 A153413 #2 Mar 31 2012 12:38:18
%S A153413 3,5,29,59,137,179,239,419,617,1049,1607,1697,1787,2267,2309,2729,
%T A153413 3257,3389,3527,3767,4157,4217,4337,4799,5639,5867,6659,6689,6869,
%U A153413 6959,7487,7547,7589,8537,8627,8969,9629,9857,9929,10457,11117,11969,12539,13337
%N A153413 Smaller of twin prime pairs such that p1*p2+average_of_twin_prime_pair=prime.
%C A153413 3*5+4=19 prime, 5*7+6=41 prime, 29*31+30=929 prime, ...
%t A153413 lst={};Do[p1=Prime[n];p2=Prime[n+1];If[p2-p1==2,a=p1*p2+(p1+1);If[PrimeQ[a],AppendTo[lst,p1]]],{n,7!}];lst
%Y A153413 Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410
%K A153413 nonn
%O A153413 1,1
%A A153413 _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008