Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.1

Powers of Two Modulo Powers of Three

Michael Coons and Heath Winning
School of Mathematical and Physical Sciences
The University of Newcastle
Callaghan, NSW


Since 2 is a primitive root of 3m for each positive integer m, the set of points { (n, 2n mod 3m) : n ≥ 0}, viewed as a subset of Z≥ 0 × Z≥ 0 is bi-periodic, with minimal periods ϕ(3m) (horizontally) and 3m (vertically). We show that if one considers the classes of n modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of Stoneham numbers.

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(Concerned with sequences A000079 A000244.)

Received May 11 2015; revised version received May 18 2015. Published in Journal of Integer Sequences, May 29 2015.

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