A special case of nim played by the following rules. Given a heap of size 
,
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 nim-values for this game.
The first few values of Grundy's game are 0, 0, 0, 1, 0, 2, 1, 0, 2, ... (OEIS A002188).
Grundy's Game
See also
Nim-ValueExplore with Wolfram|Alpha
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 "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Grundy's GameCite this as:
Weisstein, Eric W. "Grundy's Game." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GrundysGame.html