Journal of Integer Sequences, Vol. 24 (2021), Article 21.7.5

Appearance of Primes in Fourth-Order Odd Divisibility 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


Let (An) denote any odd, non-degenerate, non-null, fourth-order linear divisibility sequence and let p be any prime such that p divides some term An (n > 1) of (An). In this paper we derive a number of properties of (An). In particular, we exhibit conditions which guarantee that if p | Ak, then ω | k. Here ω (= ω(p)) is the least positive integer m such that p | Am.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A005013 A056570 A127595 A215465 A215466 A238536 A238537 A238538.)

Received April 7 2021; revised versions received June 5 2021; June 22 2021. Published in Journal of Integer Sequences, July 1 2021.

Return to Journal of Integer Sequences home page