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A linear recurrence sequence of composite numbers

Part of: Sequences and sets Computational number theory

Published online by Cambridge University Press:  01 November 2012

Jonas Šiurys
Jonas Šiurys*
Affiliation:
Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania (email: jonas.siurys@gmail.com)

Abstract

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We prove that for each positive integer k in the range 2≤k≤10 and for each positive integer k≡79 (mod 120) there is a k-step Fibonacci-like sequence of composite numbers and give some examples of such sequences. This is a natural extension of a result of Graham for the Fibonacci-like sequence.

MSC classification

Secondary: 11B37: Recurrences 11B39: Fibonacci and Lucas numbers and polynomials and generalizations 11B50: Sequences (mod $m$) 11Y55: Calculation of integer sequences
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 360 - 373
Copyright
Copyright © London Mathematical Society 2012

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