login
Worst cases for Pierce expansions (numerators).
(Formerly M0585)
2

%I M0585 #28 Dec 17 2015 02:56:10

%S 1,2,3,4,7,12,22,30,32,61,65,115,161,189,296,470,598,841,904,1856,

%T 2158,2416,1925,3462,2130,3749,6546,11201,2159,2360,5186,6071,8664,

%U 14735,59745,68482,117997,175672,268618,135585,178909,314752,490652,76800,116789,125493,290641,540539,831180

%N Worst cases for Pierce expansions (numerators).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Hiroaki Yamanouchi, <a href="/A006537/b006537.txt">Table of n, a(n) for n = 1..57</a>

%H P. Erdős and Jeffrey Shallit, <a href="http://archive.numdam.org/ARCHIVE/JTNB/JTNB_1991__3_1/JTNB_1991__3_1_43_0/JTNB_1991__3_1_43_0.pdf">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

%H Vlado Keselj, <a href="http://www.cs.uwaterloo.ca/research/tr/1996/21/cs-96-21.pdf">Length of finite Pierce series: theoretical analysis and numerical computations</a>, Dept. Computer Science, U Waterloo, CS-96-21, Sep 10 1996.

%H M. E. Mays, <a href="http://www.fq.math.ca/Scanned/25-3/mays.pdf">Iterating the division algorithm</a>, Fib. Quart., 25 (1987), 204-213.

%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>

%Y See A006538 for denominators.

%K nonn,frac

%O 1,2

%A _Jeffrey Shallit_, _N. J. A. Sloane_

%E a(38)-a(49) (from Keselj report) added by _R. J. Mathar_, Jun 30 2008