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 A189153 #15 Aug 03 2014 14:01:30
%S A189153 2,4,6,8,22,51,118,313,796,2022,5460,14756,41508,116504,331022,944930,
%T A189153 2716758,7851206
%N A189153 The number of primes in A013918 less than 10^n.
%C A189153 It seems that sequence A013918 is infinite, but this has never been proved.
%F A189153 Let x=10^n, then a(n) has the asymptotic expression a(n)~0.475*li( sqrt(4x/log(4x)) )
%t A189153 p = Select[Accumulate[Prime[Range[100000]]], PrimeQ]; Table[Length[Select[p, # < 10^n &]], {n, Floor[Log[10., p[[-1]]]]}] (* _T. D. Noe_, Apr 19 2011 *)
%o A189153 (PARI)
%o A189153 PrimesInSumOfPrimes(n)=
%o A189153 {
%o A189153 local(p, s, w);
%o A189153 p=s=w=0;
%o A189153 while( s<=10^n,
%o A189153 if( isprime(s), w++ );
%o A189153 p = nextprime(p+1);
%o A189153 s = s + p;
%o A189153 );
%o A189153 return(w);
%o A189153 }
%Y A189153 Cf. A007504, A013918.
%K A189153 nonn
%O A189153 1,1
%A A189153 _Henryk Dabrowski_, Apr 17 2011