A004796 -id:A004796 - cp's OEIS frontend

A087460 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.

2, 3, 4, 10, 11, 30, 83, 226, 4549, 91379, 91380, 248396, 248397, 675213, 4989190, 4989191, 13562026, 13562027, 36865412, 100210580, 2012783315, 5471312310, 40427833595, 40427833596, 109894245428, 812014744421, 812014744422, 2207284924202, 2207284924203

Offset: 2

Robert G. Wilson v, Sep 03 2003

nonn

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

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.

Cf. A002387, A004796.

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}]

Corrected and extended by Steven J. Kifowit, May 26 2015

cp's OEIS Frontend

A087460 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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions