%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