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 A160917 #15 Dec 29 2019 08:40:04
%S A160917 60,282,348,522,570,618,1788,2112,4050,4422,5880,6198,8232,9678,10458,
%T A160917 11700,12072,12162,12378,14010,16140,17598,17838,21648,22698,33348,
%U A160917 36342,39228,41610,43782,44088,46272,48780,51198,53088,56910,58230
%N A160917 Averages of twin prime pairs which can be represented as a sum of three consecutive of such pair averages.
%C A160917 Values A014574(j) of the form A014574(k)+A014574(k+1)+A014574(k+2).
%H A160917 Amiram Eldar, <a href="/A160917/b160917.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%e A160917 a(1) = 60 = A014574(7) = 12 + 18 + 30 = A014574(3) + A014574(4) + A014574(5).
%e A160917 a(2) = 282 = A014574(19) = 72 + 102 + 108 = A014574(8) + A014574(9) + A014574(10).
%t A160917 PrimeNextTwinAverage[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k-1]||!PrimeQ[k+1], k++ ];k];lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],a=n;b=PrimeNextTwinAverage[a]; c=PrimeNextTwinAverage[b];a=a+b+c;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst, a]]],{n,8!}];lst
%t A160917 Module[{m=Mean/@Select[Partition[Prime[Range[10000]],2,1],#[[2]]-#[[1]] == 2&],t},t=Total/@Partition[m,3,1];Intersection[m,t]] (* _Harvey P. Dale_, Mar 06 2018 *)
%Y A160917 Cf. A014574, A160916, A160918.
%K A160917 nonn
%O A160917 1,1
%A A160917 _Vladimir Joseph Stephan Orlovsky_, May 30 2009
%E A160917 Comments moved to the examples - _R. J. Mathar_, Sep 11 2009