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 A103762 #35 Sep 01 2024 04:02:07
%S A103762 1,4,7,10,12,15,18,20,23,26,29,31,34,37,39,42,45,48,50,53,56,58,61,64,
%T A103762 67,69,72,75,77,80,83,86,88,91,94,97,99,102,105,107,110,113,116,118,
%U A103762 121,124,126,129,132,135,137,140,143,145,148,151,154,156,159,162
%N A103762 a(n) = least k with Sum_{j = n..k} 1/j >= 1.
%C A103762 a(n) = A136617(n) + n for n > 1. Also a(n) = A136616(n-1) + 1 for n > 1.
%C A103762 If you compare this to floor(e*n) = A022843, 2,5,8,10,13,16,..., it appears that floor(e*n)-a(n) = 1,1,1,0,1,1,1,1,1,1,0,..., initially consisting of 0's and 1's. The places where the 0's occur are 4, 11, 18, 25, 32, 36, 43, 50, 57, 64, 71, ... whose differences seem to be 4, 7 or 11.
%C A103762 There are some rather sharp estimates on this type of differences between harmonic numbers in Theorem 3.2 of the Sintamarian reference, which may help to uncover such a pattern. - _R. J. Mathar_, Apr 15 2008
%C A103762 a(n) = round(e*(n-1/2)) with the exception of the terms of A277603; at those values of n, a(n) = round(e*(n-1/2)) + 1. - _Jon E. Schoenfield_, Apr 03 2018
%H A103762 T. D. Noe, <a href="/A103762/b103762.txt">Table of n, a(n) for n = 1..1000</a>
%H A103762 E. R. Bobo, <a href="http://www.jstor.org/stable/2687034">A sequence related to the harmonic series</a>, College Math. J. 26 (1995), 308-310.
%H A103762 D. T. Clancy and S. J. Kifowit, <a href="http://dx.doi.org/10.4169/college.math.j.45.3.199">A closer look at Bobo's sequence</a>, College Math. J. 45 (2014), 199-206.
%H A103762 A. Sintamarian, <a href="http://dx.doi.org/10.1007/s11075-007-9132-0">A generalization of Euler's constant</a>, Numer. Algor. 46 (2007), pp. 141-151.
%t A103762 i = 0; s = 0; Table[While[s < 1, i++; s = s + 1/i]; s = s - 1/n; i, {n, 100}] (* _T. D. Noe_, Jun 26 2012 *)
%o A103762 (PARI) default(realprecision, 10^5); e=exp(1);
%o A103762 a(n) = if(n<2, 1, floor(e*n+(1-e)/2+(e-1/e)/(24*n-12))); \\ _Jinyuan Wang_, Mar 06 2020
%Y A103762 Cf. A136616, A136617, A242679 (Bobo numbers).
%Y A103762 Cf. A081881, A277603, A289183. - _Jon E. Schoenfield_, Mar 31 2018
%K A103762 nonn
%O A103762 1,2
%A A103762 _David W. Wilson_, Apr 14 2008