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Omni-MATH / There are n stones in a heap. Two players play the game by alternatively taking either 1 stone from the heap or a prime number of stones which divides the current number of stones …

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problem

There are nn{} stones in a heap. Two players play the game by alternatively taking either 1 stone from the heap or a prime number of stones which divides the current number of stones in the heap. The player who takes the last stone wins. For which nn{} does the first player have a strategy so that he wins no matter how the other player plays?
Plain-text mathematical notation (without MathML)
There are n stones in a heap. Two players play the game by alternatively taking either 1 stone from the heap or a prime number of stones which divides the current number of stones in the heap. The player who takes the last stone wins. For which n does the first player have a strategy so that he wins no matter how the other player plays?
Original LaTeX notation
There are $n{}$ stones in a heap. Two players play the game by alternatively taking either 1 stone from the heap or a prime number of stones which divides the current number of stones in the heap. The player who takes the last stone wins. For which $n{}$ does the first player have a strategy so that he wins no matter how the other player plays?

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Source and history

task_id
dea3843c-cf1e-5c9d-b59a-42cc8aa99ca2
task_key
test--dea3843c-cf1e-5c9d-b59a-42cc8aa99ca2
task_revision_id
1
config / split
/ test

Official source

initial import