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Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/3.
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%I #16 Mar 08 2023 09:58:59

%S 1,2,3,6,16,59,400,6467,361139,114916199

%N Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/3.

%C a(n) <= e^(e^(n/3)), therefore a(10) < 1492725701441. - _Stefan Steinerberger_, Mar 18 2006

%C a(11) > 5*10^10. - _Robert Price_, Dec 10 2013

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicSeriesofPrimes.html">Harmonic Series of Primes</a>

%t Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];

%t m, {n, 1, 10}] (* _Robert Price_, Mar 27 2019 *)

%Y Cf. A016088, A046024, A103591-A103600.

%K nonn,more

%O 1,2

%A _James R. Buddenhagen_, Mar 28 2005

%E a(10) from _Robert Price_, Dec 10 2013