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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 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.)