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 A357923 #23 Dec 12 2022 22:30:30 %S A357923 1,3,17,68,242,812,2619,8224,25345,77006,231355,688758,2034965, %T A357923 5973932,17441201,50678536,146643235,422769139,1214857227,3480786068, %U A357923 9946872233,28357093263,80667175724,229020154166,649028530125,1836242560272,5187142333288,14632132586005 %N A357923 a(n) is the least number of terms in the sum S = 1/(n+1) + 1/(n+2) + 1/(n+3) + ... such that S > n. %F A357923 From _Thomas Scheuerle_, Nov 30 2022: (Start) %F A357923 a(n) ~ ceiling(exp(n + digamma(1+n)) - (1/2) - n). %F A357923 floor(digamma(a(n)+n+1) - digamma(n+1)) = n. (End) %e A357923 For n=0, a single term suffices: S = 1/1 > n = 0. %e A357923 For n=1, a(1) = 3 terms suffice: S = 1/2 + 1/3 + 1/4 > n = 1. %e A357923 For n=2, a(3) = 17 terms suffice: S = 1/3 + ... + 1/19 > 2. %Y A357923 Cf. A002387, A358464. %K A357923 nonn %O A357923 0,2 %A A357923 _Gil Broussard_, Oct 20 2022 %E A357923 a(18)-a(27) from _Jon E. Schoenfield_, Nov 30 2022