Jump to ContentJump to Main Navigation
Show Summary Details
More options …



Mathematical Citation Quotient (MCQ) 2017: 0.20

See all formats and pricing
More options …

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


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.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

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

Comments (0)

Please log in or register to comment.
Log in