Journal of Integer Sequences, Vol. 16 (2013), Article 13.9.3

Rumor Arrays

Bruce Dearden, Joel Iiams, and Jerry Metzger
University of North Dakota
Department of Mathematics
Witmer Hall Room 313
101 Cornell Street Stop 8376
Grand Forks, ND 58202-8376


Rumor sequences are generated recursively as follows: fix nonnegative integers b, c, and let z0 = 0. For n ≥ 1, define zn = (bzn-1 + c) mod n, where the least nonnegative residue modulo n is taken. There have been a few papers dealing with the behavior of rumor sequences, but they all concern that behavior when the value of c is fixed. It turns out that if, for a given value of b, the rumor sequences for c = 0,1,2,... are written down, one below the other, some interesting and unexpected patterns appear in the columns of that array. These patterns are investigated, proving some, and, based on computer generated data, we make two conjectures.

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(Concerned with sequences A031218 A177356 A208125.)

Received March 29 2013; revised version received October 1 2013. Published in Journal of Integer Sequences, October 13 2013.

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