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Number of consecutive integers in the set of all possible values in a stochastic sequence.
1

%I #5 Jun 04 2013 12:06:27

%S 1,2,3,6,13,22,39,62,117,180,367,594,1073,1888,3567

%N Number of consecutive integers in the set of all possible values in a stochastic sequence.

%H E. Ben-Naim and P. L. Krapivsky, <a href="http://arXiv.org/abs/cond-mat/0208072">Growth and Structure of Stochastic Sequences</a>, J. Phys. A (2002).

%H E. Ben-Naim, <a href="http://cnls-www.lanl.gov/People/ebn/pubs/reccur/reccur.html">Home page</a>

%F Stochastic sequence recursive (Fibonacci-like) rule: x_n=x_{n-1}+x_p with randomly chosen p=0, ..., n-1 (x_0=1)

%F Numbers so far suggest that a(n) = A003064(n) - n + 1, n>1. - _Ralf Stephan_, Mar 21 2004

%e x_1=2 hence a(1)=1 x_2=3,4 hence a(2)=2 x_3=4,5,6,8 hence a(3)=3

%K nonn

%O 1,2

%A Eli Ben-Naim (ebn(AT)lanl.gov), Sep 19 2002