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A189153 The number of primes in A013918 less than 10^n. 1
2, 4, 6, 8, 22, 51, 118, 313, 796, 2022, 5460, 14756, 41508, 116504, 331022, 944930, 2716758, 7851206 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..18.

FORMULA

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

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 *)

PROG

(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);

}

CROSSREFS

Cf. A007504, A013918.

Sequence in context: A277258 A029951 A062287 * A194393 A119260 A219616

Adjacent sequences:  A189150 A189151 A189152 * A189154 A189155 A189156

KEYWORD

nonn

AUTHOR

Henryk Dabrowski, Apr 17 2011

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)