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 A154565 #5 Jun 13 2017 04:24:04
%S A154565 2,15,51,210,330,651,1365,1650,1926,3480,5430,5985,6501,11310,16485,
%T A154565 16590,21660,25026,27270,28635,35190,38001,39285,46905,48690,58905,
%U A154565 64170,90651,109485,143376,148995,151845,190995,311676,316251,332526
%N A154565 One-half of averages of twin prime pairs of A001318.
%H A154565 G. C. Greubel, <a href="/A154565/b154565.txt">Table of n, a(n) for n = 1..1000</a>
%t A154565 q=3;lst={};s=0;Do[s+=n/q;If[Floor[s]==s,If[PrimeQ[2*s-1]&&PrimeQ[2*s+1],AppendTo[lst,s]]],{n,0,8!}];lst
%Y A154565 Cf. A154563, A074378.
%K A154565 nonn
%O A154565 1,1
%A A154565 _Vladimir Joseph Stephan Orlovsky_, Jan 12 2009