cp's OEIS Frontend

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.

%I A281355 #61 Dec 23 2024 14:53:45
%S A281355 1,8,57,419,3092,22846,168804,1247298,9216354,68100151,503195829,
%T A281355 3718142208,27473561358,203003686106,1500005624924,11083625711271,
%U A281355 81897532160125,605145459495141,4471453748222757,33039822589391676,244133102611731231,1803913190804074904,13329215764452299411
%N 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.
%C A281355 A different way of listing the sums mentioned in A092318.
%C A281355 A092318 is the main entry for this problem.
%H A281355 Gerhard Kirchner, <a href="/A281355/b281355.txt">Table of n, a(n) for n = 1..1000</a> [replacing an older version by Vincenzo Librandi]
%H A281355 Jerry V Polfer, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2017-January/017225.html">found a new sequence, not sure if interesting, and how to properly submit</a>, Seqfan list, Jan. 22, 2017 (and follow-up messages).
%H A281355 Albert Säfström, <a href="/A281355/a281355.txt">n describes the expected number of loops created by tieing together two random loose ends of a(n) ropes until there is none left.</a>
%F A281355 Lim_{n -> oo} a(n)/exp(2*n) = 1/4e^gamma ~ 0.140364870891721292456...;
%F A281355 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]
%t A281355 a[n_]:=Floor[Exp[2*n-EulerGamma]/4+1]-Boole[n==1]; Array[a,23] (* _Stefano Spezia_, Jun 25 2024 *)
%Y A281355 Cf. A002387, A092318.
%K A281355 nonn
%O A281355 1,2
%A A281355 _N. J. A. Sloane_, Jan 22 2017, following a suggestion from _Jerry Polfer_
%E A281355 More explicit, self-contained definition by _M. F. Hasler_, Jan 22 2017
%E A281355 More terms (computed using A056053) from _M. F. Hasler_, Jan 23 2017
%E A281355 a(17) corrected in data and 127 terms in the b-file, according to the corrections in A092315, _Gerhard Kirchner_, Jul 27 2020