Journal of Integer Sequences, Vol. 23 (2020), Article 20.4.8

A Sextic Extension of the Lucas Functions

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


We develop a necessary and sufficient primality test for integers N such that N6 − 1 is divisible by a large power of 7, based on the properties of two linear recurrence sequences of order 6. These two sequences are analogous to the well-known Lucas sequences. In addition, we provide tables from which it is easy to compute the characteristic polynomial of the sequences.

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(Concerned with sequences A001351 A001945 A005120 A006235 A180510.)

Received February 27 2020; revised versions received March 2 2020; May 5 2020; May 6 2020. Published in Journal of Integer Sequences, May 6 2020.

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