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A285304 P-positions in the sum-from-product game. 2
1, 2, 3, 4, 5, 7, 11, 13, 16, 17, 19, 22, 23, 25, 27, 29, 31, 32, 34, 37, 41, 43, 46, 47, 49, 52, 53, 55, 57, 59, 61, 64, 67, 71, 73, 74, 79, 81, 82, 83, 85, 88, 89, 92, 94, 97, 101, 103, 106, 107, 109, 113, 115, 117, 119, 121, 125, 127, 131, 134, 136, 137, 139, 141, 142, 145, 149, 151, 157, 158, 163, 167, 169, 171, 173, 175, 178, 179, 181, 185, 187, 189, 190, 191, 193, 194, 196, 197, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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 nonnegative. That is, the next player starts with a new number n - a - b. A player without a move loses.
Prime numbers are P-positions.
N-positions are A285847.
LINKS
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.
CROSSREFS
Cf. A285847.
Sequence in context: A139316 A062972 A231878 * A036844 A284696 A033070
KEYWORD
nonn
AUTHOR
Tanya Khovanova and students, May 06 2017
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)