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 A223037 #14 Apr 17 2013 14:16:48
%S A223037 3,271,5195969,1801241230056600467
%N A223037 a(n) = largest prime p such that Sum_{primes q = 2, ..., p} 1/q does not exceed n.
%C A223037 Since Sum_{prime q} 1/q diverges, the sequence is infinite.
%C A223037 In fact, by the Prime Number Theorem Prime(k) ~ k log k as k -> infinity, and by integration Sum_{k <= n} 1/(k log k) ~ log log n, so a(n) ~ Prime(Floor(e^e^n)).
%C A223037 a(4) = A000040(A046024(4)-1) = Prime[43922730588128389], but Mathematica 7.0.0 cannot compute this prime on a Mac computer running OS X.
%C A223037 Instead, using a(4) = largest prime < A016088(4) = 1801241230056600523, Mathematica's PrimeQ function finds that a(4) = 1801241230056600467.
%C A223037 See A016088 for other relevant comments, references, links, and programs.
%F A223037 a(n) = A000040(A046024(n)-1) = largest prime < A016088(n).
%F A223037 a(n) ~ Prime(Floor(e^e^n)) = A000040(A096232(n)) as n -> infinity.
%e A223037 a(1) = 3 because 1/2 + 1/3 < 1 < 1/2 + 1/3 + 1/5.
%Y A223037 Cf. A016088, A046024, A024451, A096232.
%K A223037 nonn,hard,more
%O A223037 1,1
%A A223037 _Jonathan Sondow_, Apr 16 2013