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 A153089 #7 Jan 15 2013 10:51:20
%S A153089 2,7,117241,1351781,3703429,243729623,486707171,568561471,766634423,
%T A153089 883314979,1058403331,1520509423,1933700891,1997566367,2063533819,
%U A153089 2632011079,3040681037,3591772153,4114380107,7870826569,8414671219
%N A153089 Continue with summing & priming the A013918 list.
%C A153089 If level 1 sum primes is the prime number list A000040, and level 2 sum primes is the list A013918 then the above list is level 3.
%C A153089 Continue with summing & priming for Level 4 sum primes which are
%C A153089 2, 50575480511, 158413287841, 379787123171, 88082548147771, 3939163325960453, 4342203121792903, 41672041797268133, 92013021551247323, 145937058697288751, 157891295660264779, 270930872865589619,...
%C A153089 Again continue with summing & priming for Level 5 sum primes which are
%C A153089 2, 50575480513, 1663807730918617976723, 14304824932873646803553, 28817336920092499216069, 20284632396728311969809131, 168804229342169123733371839, 909257309497199880752121319,...
%C A153089 Again continue with summing & priming for Level 6 sum primes which are
%C A153089 2, @Prime[1]
%C A153089 22388562459746799685433396747, @Prime[57000046]
%C A153089 ????
%C A153089 Initially found using Mathematica then a NTL+C program using Miller-witness 10 trials. Checked summed primes with PrimeQ[].
%H A153089 M. J. Crowe, <a href="/A153089/b153089.txt">Table of n, a(n) for n = 1..10000</a>
%t A153089 lst2={}; s2=0; Do[s2=s2+Prime[n]; If[PrimeQ[s2], AppendTo[lst2, s2]], {n, 4700}]; lst3={}; s3=0; Do[s3=s3+lst2[[n]];If[PrimeQ[s3], AppendTo[lst3, s3]], {n,1,Length[lst2]}]; lst3
%Y A153089 Cf. A000040, A013918.
%K A153089 nonn
%O A153089 1,1
%A A153089 Michael J. Crowe (michaelcrowe117(AT)btinternet.com), Dec 18 2008