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 A155851 #4 Jun 22 2015 16:45:58
%S A155851 5,23,53,233,563,1259,2579,2909,12713,22543,28099,31729,39607,41017,
%T A155851 42463,87511,110359,115279,117787,138863,141671,213533,242243,257353,
%U A155851 265117,269069,289171,310019,318557,327193,331603,354097,372607,441101
%N A155851 n is prime and is the sum of the first k primes for some k, start from 5.
%C A155851 Analogous to A013918, A071151. Number '5' is first prime number after first composite number '4'.
%t A155851 s=0;lst={};Do[p=Prime[n];s+=p;If[PrimeQ[s],AppendTo[lst,s]],{n,3,7!}];lst
%t A155851 Select[Accumulate[Prime[Range[3,500]]],PrimeQ] (* _Harvey P. Dale_, Jun 22 2015 *)
%Y A155851 Cf. A013918, A071151
%K A155851 nonn
%O A155851 1,1
%A A155851 _Vladimir Joseph Stephan Orlovsky_, Jan 28 2009