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 A153375 #6 Aug 09 2014 15:17:44
%S A153375 7,17,1049,2767,3347,22391,45989,88237,92333,135241,154157,233327,
%T A153375 287159,344231,365297,392737,479639,549749,574367,650591,659437,
%U A153375 666089,749807,786959,869069,959737,1023541,1045043,1161851,1180427,1193041
%N A153375 Larger of two consecutive prime numbers such that p0+p1=average of twin prime pairs and p0*p1+7=average of twin prime pairs.
%C A153375 5+7=12+-1=primes, 5*7+7=42+-1=primes; 13+17=30+-1=primes, 13*17+7=228+-1=primes;...
%H A153375 Harvey P. Dale, <a href="/A153375/b153375.txt">Table of n, a(n) for n = 1..1000</a>
%t A153375 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,p1]],{n,9!}];lst
%t A153375 atpQ[{a_,b_}]:=Module[{t=a+b,p=a*b},AllTrue[{t-1,t+1,p+6,p+8},PrimeQ]]; Transpose[ Select[Partition[Prime[Range[100000]],2,1],atpQ]][[2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 09 2014 *)
%Y A153375 Cf. A099349, A153374
%K A153375 nonn
%O A153375 1,1
%A A153375 _Vladimir Joseph Stephan Orlovsky_, Dec 24 2008