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 A165286 #5 Jun 11 2015 10:52:30
%S A165286 23,61,83,101,139,157,197,263,283,293,331,349,367,383,401,449,491,509,
%T A165286 541,569,571,577,641,659,661,701,751,773,809,811,853,859,881,887,967,
%U A165286 977,997,1009,1039,1069,1117,1123,1181,1193,1217,1237,1279,1283,1361
%N A165286 Primes which are the sum of two or more consecutive terms of A072055.
%C A165286 The terms in A072055 are odd, so the count of terms in the sum must be odd to yield a prime.
%e A165286 a(1)= 5+7+11 = sum_{i=1..3} A072055(i) = 23.
%e A165286 a(2) = sum_{i=1..5} A072055(i) = 5+7+11+15+23 = 61. a(3) = 7+11+15+23+27 = 83.
%t A165286 lst={};Do[s=2*Prime[m]+1;Do[p=Prime[n];s+=(2*p+1);If[PrimeQ[s], If[s<=6949, AppendTo[lst,s]]],{n,m+1,6!}],{m,1,6!}];lst=Take[Union@lst,200]
%t A165286 Module[{nn=100,terms},terms=2*Prime[Range[nn]]+1;Take[Union[Select[ Flatten[ Table[Total/@Partition[terms,n,1],{n,3,nn,2}]],PrimeQ]],nn/2]] (* _Harvey P. Dale_, Jun 11 2015 *)
%Y A165286 Cf. A165285
%K A165286 nonn
%O A165286 1,1
%A A165286 _Vladimir Joseph Stephan Orlovsky_, Sep 13 2009
%E A165286 Redefined in terms of A072055; cross-references to unrelated sequences deleted - _R. J. Mathar_, Sep 16 2009