An Aperiodic Subtraction Game of Nim-Dimension Two

摘要

In a recent manuscript, Fox studied infinite subtraction games with a finite (ternary) and aperiodic Sprague-Grundy function. Here we provide an elementary example of a game with the given properties, namely the game given by the subtraction set {F2n+1 - 1}, where Fi is the ith Fibonacci number, and n ranges over the positive integers.