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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 (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 for n>1.

If you compare this to floor[e*n] = A022843, 2,5,8,10,13,16,..., it appears that [en]-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.

Comment from R. J. Mathar, Apr 15 2008: 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.

REFERENCES

Daniel T. Clancy and Steven J. Kifowit, A Closer Look at Bobo's Sequence, College Math. J., 45 (2014), 199-206.

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.

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 *)

CROSSREFS

Cf. A136616, A136617, A242679 (Bobo numbers).

Sequence in context: A078633 A190008 A184911 * A186226 A080734 A104280

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 October 21 00:56 EDT 2017. Contains 293679 sequences.