A285304 P-positions in the sum-from-product game.

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

Offset: 1

Author

Tanya Khovanova and students, May 06 2017

Keywords

• nonn

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.