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Purely Periodic Three-move Subtraction Games
We determine the full Sprague-Grundy sequence and its least period for a class of three-move subtraction games whose sequences are periodic from the start. Write the move set as $S=\{a,b,c\}$, with $0<a<b<c$ and $\gcd(a,b,c)=1$. The case $a=1$ is known and is summarized separately. For $a\ge2$ and $
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