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