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 A153374 #2 Mar 31 2012 12:38:18
%S A153374 5,13,1039,2753,3343,22381,45979,88223,92317,135221,154153,233323,
%T A153374 287149,344221,365293,392723,479629,549739,574363,650581,659423,
%U A153374 666079,749803,786949,869059,959723,1023521,1045027,1161841,1180423,1193021
%N A153374 Smaller of two consecutive prime numbers such that p0+p1=average of twin prime pairs and p0*p1+7=average of twin prime pairs.
%C A153374 5+7=12+-1=primes, 5*7+7=42+-1=primes; 13+17=30+-1=primes, 13*17+7=228+-1=primes;...
%t A153374 lst={};Do[p0=Prime[n];p1=Prime[n+1];a=p0+p1;b=p0*p1+7;If[PrimeQ[a-1]&&PrimeQ[a+1]&&PrimeQ[b-1]&&PrimeQ[b+1],AppendTo[lst,p0]],{n,9!}];lst
%Y A153374 Cf. A099349
%K A153374 nonn
%O A153374 1,1
%A A153374 _Vladimir Joseph Stephan Orlovsky_, Dec 24 2008