OFFSET
1,1
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 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.
P-positions are A285304.
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and students, May 06 2017
STATUS
approved