Journal of Integer Sequences, Vol. 21 (2018), Article 18.3.5

On Some Combinations of Non-Consecutive Terms of a Recurrence Sequence

Eva Trojovská
Department of Mathematics
Faculty of Science
University of Hradec Králové
Czech Republic


Let (Gm)m≥0 be an integer linear recurrence sequence (satisfying some weak technical conditions) and let x ≥ 1 be an integer. In this paper, among other things, we are interested in non-consecutive combinations xGn+a + Gn that belong to the sequence (Gm)m≥0 for infinitely many positive integers n. In this case, we make explicit an upper bound for x that depends only on a and the zeros of the characteristic polynomial of this recurrence (this generalizes previous papers of Trojovský). As an application, we study the Fibonacci case.

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(Concerned with sequence A000045.)

Received February 19 2018; revised version received March 11 2018. Published in Journal of Integer Sequences, March 12 2018.

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