This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103593 #17 Feb 16 2025 08:32:56
%S A103593 1,2,3,6,16,59,400,6467,361139,114916199
%N A103593 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/3.
%C A103593 a(n) <= e^(e^(n/3)), therefore a(10) < 1492725701441. - _Stefan Steinerberger_, Mar 18 2006
%C A103593 a(11) > 5*10^10. - _Robert Price_, Dec 10 2013
%H A103593 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicSeriesofPrimes.html">Harmonic Series of Primes</a>
%t A103593 Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/3, m++];
%t A103593 m, {n, 1, 10}] (* _Robert Price_, Mar 27 2019 *)
%Y A103593 Cf. A016088, A046024, A103591-A103600.
%K A103593 nonn,more
%O A103593 1,2
%A A103593 _James R. Buddenhagen_, Mar 28 2005
%E A103593 a(10) from _Robert Price_, Dec 10 2013