Geodesic
An aperiodic subtraction game of Nim-dimension two
Journal of integer sequences, Tome 18 (2015) no. 7
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 ${F_{2n+1} - 1}$, where $F_{i}$ is the $i$th Fibonacci number, and $n$ ranges over the positive integers.
Classification : 91A46, 11B39
Keywords: subtraction game, Fibonacci number, sprague-Grundy function 
@article{JIS_2015__18_7_a4,
     author = {Larsson,  Urban and Fox,  Nathan},
     title = {An aperiodic subtraction game of {Nim-dimension} two},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {7},
     zbl = {1397.91104},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a4/}
}
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Larsson,  Urban; Fox,  Nathan. An aperiodic subtraction game of Nim-dimension two. Journal of integer sequences, Tome 18 (2015) no. 7. http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a4/