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

1,2

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

Table of n, a(n) for n=1..89.

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 A396594

Adjacent sequences: A285301 A285302 A285303 * A285305 A285306 A285307

Keyword

nonn

Author

Tanya Khovanova and students, May 06 2017

Status

approved