Geodesic
The shape of the value sets of linear recurrence sequences
Journal of integer sequences, Tome 12 (2009) no. 3
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.
Classification : 11B37, 11J71
Keywords: linear recurrence sequence, value set, Kronecker's approximation theorem 
@article{JIS_2009__12_3_a6,
     author = {Gerhold,  Stefan},
     title = {The shape of the value sets of linear recurrence sequences},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {3},
     zbl = {1258.11016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_3_a6/}
}
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Gerhold,  Stefan. The shape of the value sets of linear recurrence sequences. Journal of integer sequences, Tome 12 (2009) no. 3. http://geodesic.mathdoc.fr/item/JIS_2009__12_3_a6/