|Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.8|
Acton-Boxborough Regional High School
Acton, MA 01719
We show that the game of Nim can be viewed as a cellular automaton, where the total number of counters divided by 2 can be considered as a generation in which P-positions are born. We prove that the three-pile Nim sequence enumerated by the total number of counters is a famous toothpick sequence based on the Ulam-Warburton cellular automaton. We introduce 10 new sequences.
(Concerned with sequences
Received May 22 2014; revised version received July 13 2014. Published in Journal of Integer Sequences, July 14 2014.