If is a Recurrence Sequence, then the set of all such that is the union of a finite (possibly Empty) set and a finite number (possibly zero) of full arithmetical progressions, where a full arithmetic progression is a set of the form with
Myerson, G. and van der Poorten, A. J. ``Some Problems Concerning Recurrence Sequences.'' Amer. Math. Monthly
102, 698-705, 1995.