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A285304 P-positions in the sum-from-product game. 1
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

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 A033070

Adjacent sequences:  A285301 A285302 A285303 * A285305 A285306 A285307

KEYWORD

nonn

AUTHOR

Tanya Khovanova and students, May 06 2017

STATUS

approved

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Last modified September 25 23:23 EDT 2020. Contains 337346 sequences. (Running on oeis4.)