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Rumor Arrays
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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

USA

**Abstract:**

Rumor sequences are generated recursively as follows: fix nonnegative
integers *b*, *c*, and let *z*_{0} = 0. For
*n* ≥ 1, define *z*_{n} =
(*b**z*_{n-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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Full version: pdf,
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Mathematica code: cdf
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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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