Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.2

Some Arithmetic Properties of Certain Sequences

E. L. Roettger
Department of General Education
Mount Royal University
4825 Mount Royal Gate SW
Calgary, AB T3E 6K6

H. C. Williams
Department of Mathematics and Statistics
University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4


In an earlier paper it was argued that two sequences, denoted by {Un} and {Wn}, constitute the sextic analogues of the well-known Lucas sequences {un} and {vn}. While a number of the properties of {Un} and {Wn} were presented previously, several arithmetic properties of these sequences were only mentioned in passing. In this paper we discuss the derived sequences {Dn} and {En}, where Dn = gcd(Wn - 6 Rn,Un) and En = gcd(Wn,Un), in greater detail and show that they possess many number-theoretic properties analogous to those of {un} and {vn}, respectively.

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Received February 5 2015; revised version received May 11 2015; May 29 2015. Published in Journal of Integer Sequences, May 30 2015.

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