|Journal of Integer Sequences, Vol. 8 (2005), Article 05.1.3|
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Abstract: Given positive integers and , we write for the integer whose base- representation is the concatenation of the base- representations of . In this paper, we prove that if is a binary recurrent sequence of integers satisfying some mild hypotheses, then for every fixed integer , there are at most finitely many nonnegative integers such that is a member of the sequence . In particular, we compute all such instances in the special case that , , and is the sequence of Fibonacci numbers.
Received August 30 2004; revised version received January 13 2005. Published in Journal of Integer Sequences January 14 2005. Small revisions, January 17 2005.