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 A153128 #3 Mar 31 2012 12:38:18
%S A153128 11,31,41,67,131,3121,4229,13159,14081,24631,49877,64921,71789,127051,
%T A153128 154871,178621,249677,260011,350729,401473,487397,537883,567767,
%U A153128 718423,724499,763621,1004987,1016611,1043951,1053529,1090949,1295113,1309907
%N A153128 Prime numbers such that the sum of any 2 or 4 consecutive terms are averages of twin prime pairs and sum of any 3 or 5 consecutive terms are primes.
%t A153128 a=11;b=31;c=41;d=67;lst={a,b,c,d};Do[z=a+b+c+d+n;y=c+d+n;If[PrimeQ[z]&&n>d&&PrimeQ[n]&&PrimeQ[y]&&PrimeQ[a+b-1]&&PrimeQ[a+b+1]&&PrimeQ[b+c-1]&&PrimeQ[b+c+1]&&PrimeQ[c+d-1]&&PrimeQ[c+d+1]&&PrimeQ[d+n-1]&&PrimeQ[d+n+1]&&PrimeQ[a+b+c+d-1]&&PrimeQ[a+b+c+d+1]&&PrimeQ[b+c+d+n-1]&&PrimeQ[b+c+d+n+1],AppendTo[lst,n];a=b;b=c;c=d;d=n],{n,0,10!}];lst
%Y A153128 Cf. A153065, A062391, A153075
%K A153128 nonn
%O A153128 1,1
%A A153128 _Vladimir Joseph Stephan Orlovsky_, Dec 19 2008