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

1,2

Links

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

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A074599, A025547.

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

Sequence in context: A246939 A122996 A343364 * A092315 A229248 A242159

Adjacent sequences: A092315 A092316 A092317 * A092319 A092320 A092321

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2004

Extensions

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

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

Status

approved