A227763 Winning positions in the misere version of the Subtract-a-Prime game.

1, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset

1,2

Comments

Consider the following game: two players make moves in turn, initially the number on the board is n. Each move consists of subtracting a prime number that is at most the number on the board. The player who cannot play wins. This sequence is the set of winning positions in this game.

Links

Table of n, a(n) for n=1..66.

Mathematica

moves[n_]:= Table[n - Prime[i], {i, 1, PrimePi[n]}]; gana[n_]:= gana[n] = If[n < 2, True, !Select[moves[n], !gana[#]&]=={}]; Select[Range[155], gana[#] &]

Crossrefs

Cf. A227691, A025043, A227764.

Sequence in context: A287961 A030791 A306298 * A039091 A189817 A214420

Adjacent sequences: A227760 A227761 A227762 * A227764 A227765 A227766

Keyword

nonn

Author

José María Grau Ribas, Jul 29 2013

Status

approved