A189153 The number of primes in A013918 less than 10^n.

2, 4, 6, 8, 22, 51, 118, 313, 796, 2022, 5460, 14756, 41508, 116504, 331022, 944930, 2716758, 7851206

Offset: 1

Author

Henryk Dabrowski, Apr 17 2011

Keywords

• nonn

Comments

It seems that sequence A013918 is infinite, but this has never been proved.

Crossrefs

Cf. A007504, A013918.

Programs

Mathematica

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 *)

PARI

PrimesInSumOfPrimes(n)=
{
local(p, s, w);
p=s=w=0;
while( s<=10^n,
       if( isprime(s), w++ );
       p = nextprime(p+1);
       s = s + p;
     );
return(w);
}

Formula

Let x=10^n, then a(n) has the asymptotic expression a(n)~0.475*li( sqrt(4x/log(4x)) )