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 A046024 #49 Feb 16 2025 08:32:38
%S A046024 1,3,59,361139,43922730588128390
%N A046024 a(n) = smallest k such that Sum_{ i = 1..k } 1/prime(i) exceeds n.
%C A046024 The corresponding primes prime(a(n)) are in A016088.
%C A046024 Index m for which the prime harmonic number p[ m ] := Sum[ 1/Prime[ k ],{k,1,m} ] >= n.
%H A046024 E. Bach, D. Klyve, and J. P. Sorenson, <a href="http://dx.doi.org/10.1090/S0025-5718-09-02249-2">Computing prime harmonic sums</a>, Math. Comp. 78 (2009) 2283-2305.
%H A046024 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeNumber.html">Prime Number</a>.
%H A046024 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicSeriesofPrimes.html">Harmonic Series of Primes</a>.
%F A046024 From _Jonathan Sondow_, Apr 17 2013: (Start)
%F A046024 a(n) = A000720(A016088(n)) = A000720(A096232(n))+1.
%F A046024 a(n) = e^(e^(n + O(1))), see comment in A223037. [corrected by _Charles R Greathouse IV_, Aug 22 2013] (End)
%F A046024 a(n) = A103591(2*n). - _Michel Marcus_, Aug 22 2013
%t A046024 Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) <= n, m++];
%t A046024 m, {n, 0, 4}] (* _Robert Price_, Mar 27 2019 *)
%o A046024 (PARI) a(n)=my(t); forprime(p=2,, t+=1./p; if(t>n, return(primepi(p)))) \\ _Charles R Greathouse IV_, Apr 29 2015
%Y A046024 Cf. A004080, A016088, A096232, A223037.
%Y A046024 Cf. A024451/A002110 for Sum_{i = 1..n} 1/prime(i).
%K A046024 nonn,more,nice
%O A046024 0,2
%A A046024 _Eric W. Weisstein_
%E A046024 a(4) found by Tomás Oliveira e Silva (tos(AT)det.ua.pt), using the fourth term of A016088. - Dec 14 2005
%E A046024 a(0) from _Jonathan Sondow_, Apr 16 2013