A281355 a(n) = A092318(n) + 1: Number of terms of the odd harmonic series 1 + 1/3 + 1/5 + 1/7 + ... required to reach a sum >= n.

1, 8, 57, 419, 3092, 22846, 168804, 1247298, 9216354, 68100151, 503195829, 3718142208, 27473561358, 203003686106, 1500005624924, 11083625711271, 81897532160125, 605145459495141, 4471453748222757, 33039822589391676, 244133102611731231, 1803913190804074904, 13329215764452299411

Offset: 1

Author

N. J. A. Sloane, Jan 22 2017, following a suggestion from Jerry Polfer

Keywords

• nonn

Comments

A different way of listing the sums mentioned in A092318.

A092318 is the main entry for this problem.

Links

• Gerhard Kirchner, Table of n, a(n) for n = 1..1000 [replacing an older version by Vincenzo Librandi]
• Jerry V Polfer, found a new sequence, not sure if interesting, and how to properly submit, Seqfan list, Jan. 22, 2017 (and follow-up messages).
• Albert Säfström, n describes the expected number of loops created by tieing together two random loose ends of a(n) ropes until there is none left.

Crossrefs

Cf. A002387, A092318.

Programs

Mathematica

a[n_]:=Floor[Exp[2*n-EulerGamma]/4+1]-Boole[n==1]; Array[a,23] (* Stefano Spezia, Jun 25 2024 *)

Formula

Lim_{n -> oo} a(n)/exp(2*n) = 1/4e^gamma ~ 0.140364870891721292456...;

a(n) = floor(exp(2*n-gamma)/4+1), for all given values a(n) > 1. - M. F. Hasler and Robert G. Wilson v, Jan 23 2017 [corrected by Gerhard Kirchner, Jul 25 2020]

Extensions

More explicit, self-contained definition by M. F. Hasler, Jan 22 2017

More terms (computed using A056053) from M. F. Hasler, Jan 23 2017

a(17) corrected in data and 127 terms in the b-file, according to the corrections in A092315, Gerhard Kirchner, Jul 27 2020