A092318 a(n) = smallest m such that value of odd harmonic series Sum_{j=0..m} 1/(2j+1) is >= n.

0, 7, 56, 418, 3091, 22845, 168803, 1247297, 9216353, 68100150, 503195828, 3718142207, 27473561357, 203003686105, 1500005624923, 11083625711270, 81897532160124, 605145459495140, 4471453748222756, 33039822589391675

Offset: 1

Author

N. J. A. Sloane, Feb 16 2004

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (127 terms corrected by Gerhard Kirchner)

Crossrefs

Apart from first term, same as A092315. Equals (A092317-1)/2.

Cf. A074599, A025547.

Cf. A281355 (= a(n) + 1) for a variant.

Programs

Mathematica

a[n_] := Floor[(Exp[2 n - EulerGamma] + 1/2)/4]; a[1] = 0; Array[a, 20] (* Robert G. Wilson v, Jan 25 2017 *)

PARI

A092318=n->floor(exp(2*n-Euler)/4+1/8)-(n<2) \\ Cf. comments in A092315. - M. F. Hasler, Jan 24 2017

Formula

a(n) = floor(exp(2*n-gamma)/4+1/8), for all n > 1. - M. F. Hasler and Robert G. Wilson v, Jan 22 2017

a(n) = floor(exp(2*n-gamma)/4), for all n > 1, see correction in A092315, Gerhard Kirchner, Jul 25 2020

Extensions

More terms (computed from A092317) from M. F. Hasler, Jan 22 2017

a(17) corrected by Gerhard Kirchner, Jul 26 2020