OFFSET
2,1
COMMENTS
H(36865412) = 18.000000003719931082993704481490195538573320586002
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
LINKS
Steven J. Kifowit, Table of n, a(n) for n = 2..50
M. B. Villarino, Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series, arXiv:math/0402354v5 [math.CA], 2005.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 03 2003
EXTENSIONS
Corrected and extended by Steven J. Kifowit, May 26 2015
STATUS
approved