%I #8 May 26 2015 11:24:17

%S 2,3,4,10,11,30,83,226,4549,91379,91380,248396,248397,675213,4989190,

%T 4989191,13562026,13562027,36865412,100210580,2012783315,5471312310,

%U 40427833595,40427833596,109894245428,812014744421,812014744422,2207284924202,2207284924203

%N Least n such that H(n) is closer to an integer than any H(j) with j < n; where H(n) is the harmonic number sum_{i=0..n} 1/i.

%C H(36865412) = 18.000000003719931082993704481490195538573320586002

%C The inequality, 0.5*log(n^2+n)+gamma < H(n) < 0.5*log(n^2+n)+gamma +1/(6*n^2+6*n) (see Villarino link), where gamma is the Euler-Mascheroni constant, can be used to determine terms of this sequence without directly computing the harmonic numbers. - _Steven J. Kifowit_, May 26 2015

%H Steven J. Kifowit, <a href="/A087460/b087460.txt">Table of n, a(n) for n = 2..50</a>

%H M. B. Villarino, <a href="http://arxiv.org/abs/math/0402354v5">Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series</a>, arXiv:math/0402354v5 [math.CA], 2005.

%t d = 1; s = 1; n = 2; Do[ While[s = N[s + 1/n, 50]; Abs[Round[s] - s] > d, n++ ]; Print[n]; d = Abs[Round[s] - s]; n++, {i, 2, 18}]

%Y Cf. A002387, A004796.

%K nonn

%O 2,1

%A _Robert G. Wilson v_, Sep 03 2003

%E Corrected and extended by _Steven J. Kifowit_, May 26 2015