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 A103762 a(n) = least k with Sum_{j = n..k} 1/j >= 1. 8
 1, 4, 7, 10, 12, 15, 18, 20, 23, 26, 29, 31, 34, 37, 39, 42, 45, 48, 50, 53, 56, 58, 61, 64, 67, 69, 72, 75, 77, 80, 83, 86, 88, 91, 94, 97, 99, 102, 105, 107, 110, 113, 116, 118, 121, 124, 126, 129, 132, 135, 137, 140, 143, 145, 148, 151, 154, 156, 159, 162 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = A136617(n) + n for n > 1. Also a(n) = A136616(n-1) + 1 for n > 1. 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. 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 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 E. R. Bobo, A sequence related to the harmonic series, College Math. J. 26 (1995), 308-310. D. T. Clancy and S. J. Kifowit, A closer look at Bobo's sequence, College Math. J. 45 (2014), 199-206. A. Sintamarian, A generalization of Euler's constant, Numer. Algor. 46 (2007), pp. 141-151. MATHEMATICA 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 *) PROG (PARI) default(realprecision, 10^5); e=exp(1); a(n) = if(n<2, 1, floor(e*n+(1-e)/2+(e-1/e)/(24*n-12))); \\ Jinyuan Wang, Mar 06 2020 CROSSREFS Cf. A136616, A136617, A242679 (Bobo numbers). Cf. A081881, A277603, A289183. - Jon E. Schoenfield, Mar 31 2018 Sequence in context: A078633 A190008 A184911 * A186226 A080734 A310676 Adjacent sequences: A103759 A103760 A103761 * A103763 A103764 A103765 KEYWORD nonn AUTHOR David W. Wilson, Apr 14 2008 STATUS approved

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Last modified September 21 15:36 EDT 2023. Contains 365502 sequences. (Running on oeis4.)