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Integers


Mathematical Citation Quotient (MCQ) 2016: 0.40

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Some Monoapparitic Fourth Order Linear Divisibility Sequences

Hugh C. Williams / Richard K. Guy
Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0047

Abstract.

A sequence of rational integers is said to be a divisibility sequence if whenever . If the divisibility sequence also satisfies a linear recurrence relation of order k, it is said to be a linear divisibility sequence. The best known example of a linear divisibility sequence of order 2 is the Lucas sequence , one particular instance of which is the famous Fibonacci sequence. In their extension of the Lucas functions to order 4 linear recursions, Williams and Guy showed that the order 4 analog of can have no more than two ranks of apparition for a given prime p and frequently has two such ranks, unlike the situation for , which can only have one rank of apparition. In this paper we investigate the problem of finding those sequences which have only one rank of apparition for any prime p.

Keywords: Divisibility Sequences; Rank of Apparition; Lucas Functions

About the article

Received: 2011-06-01

Accepted: 2011-12-01

Published Online: 2012-11-30

Published in Print: 2012-12-01


Citation Information: Integers, Volume 12, Issue 6, Pages 1463–1485, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0047.

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© 2012 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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[1]
E. L. Roettger, H. C. Williams, and R. K. Guy
Designs, Codes and Cryptography, 2015, Volume 77, Number 2-3, Page 515

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