A285847 N-positions in the sum-from-product game.

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

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

Table of n, a(n) for n=1..60.

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

Cf. A285304.

Sequence in context: A043373 A054047 A056653 * A231879 A062973 A070162

Adjacent sequences: A285844 A285845 A285846 * A285848 A285849 A285850

Keyword

nonn

Author

Tanya Khovanova and students, May 06 2017

Status

approved