Grundy's Game

A special case of Nim played by the following rules. Given a heap of size $n$, two players alternately select a heap and divide it into two unequal heaps. A player loses when he cannot make a legal move because all heaps have size 1 or 2. Flammenkamp gives a table of the extremal Sprague-Grundy Values for this game. The first few values of Grundy's game are 0, 0, 0, 1, 0, 2, 1, 0, 2, ... (Sloane's A002188).

References

Flammenkamp, A. ``Sprague-Grundy Values of Grundy's
Game.'' http://www.uni-bielefeld.de/~achim/grundy.html.

Sloane, N. J. A. Sequence A002188/M0044 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.