Journal of Integer Sequences, Vol. 12 (2009), Article 09.3.6

The Shape of the Value Sets of Linear Recurrence Sequences

Stefan Gerhold
Vienna University of Technology
1040 Vienna
Microsoft Research-INRIA
91893 Orsay


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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