Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.2

Conway’s RATS Sequences in Base 3

Johann Thiel
Department of Mathematical Sciences
United States Military Academy
West Point, NY 10996


We study the behavior of Conways RATS (reverse-add-then-sort) sequences in base 3. An independent proof is given of Gentges' result that all RATS sequences in base 3 are ultimately periodic. We also prove Erdős-Kac and Hardy-Ramanujan type results for the periods of such sequences.

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(Concerned with sequence A066711.)

Received May 30 2012; revised version received November 1 2012. Published in Journal of Integer Sequences, November 4 2012.

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