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A285847
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N-positions in the sum-from-product game.
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1
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6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 26, 28, 30, 33, 35, 36, 38, 39, 40, 42, 44, 45, 48, 50, 51, 54, 56, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 84, 86, 87, 90, 91, 93, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 111
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OFFSET
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1,1
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COMMENTS
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The sum-from-product game is played by two players alternating moves. Given a positive integer n, a player can choose any two integers a and b, such that ab=n. The player subtracts a+b from n, given that the result is positive. That is, the next player starts with a new number n-a-b. A player without a move loses.
Prime numbers are P-positions.
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LINKS
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Pratik Alladi, Neel Bhalla, Tanya Khovanova, Nathan Sheffield, Eddie Song, William Sun, Andrew The, Alan Wang, Naor Wiesel, Kevin Zhang Kevin Zhao, PRIMES STEP Plays Games, arXiv:1707.07201 [math.CO], 2017, Section 6.
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EXAMPLE
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Numbers 1, 2, 3, 4, 5, 7, 11 are P-positions as there are no legal moves. Therefore, 6 and 8 are N-positions, as the only move from 6 goes to 1, and the only move from 8 goes to 2. It follows that 16 is a P-position as there are two moves: 16-4-4 = 8, and 16-2-8 = 6: both are N-positions.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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