

A103762


a(n) = least k with Sum_{j = n..k} 1/j >= 1.


7



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
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OFFSET

1,2


COMMENTS

a(n) = A136617(n) + n for n > 1. Also a(n) = A136616(n) + 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*(n1/2)) with the exception of the terms of A277603; at those values of n, a(n) = round(e*(n1/2)) + 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), 308310.
D. T. Clancy and S. J. Kifowit, A closer look at Bobo's sequence, College Math. J. 45 (2014), 199206.
A. Sintamarian, A generalization of Euler's constant, Numer. Algor. 46 (2007), pp. 141151.


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 *)


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



