The Shape of the Value Sets of Linear Recurrence Sequences
Stefan Gerhold
Vienna University of Technology
1040 Vienna
Austria
and
Microsoft Research-INRIA
91893 Orsay
France
Abstract:
We show that the closure of the value set of a real linear recurrence
sequence is the union of a countable set and a finite collection of
intervals. Conversely, any finite collection of closed intervals is
the closure of the value set of some recurrence sequence.
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Received March 25 2009;
revised version received April 14 2009.
Published in Journal of Integer Sequences, April 27 2009.
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