A227764 Losing positions in the misere version of the Subtract-a-Prime game.

2, 3, 11, 12, 27, 36, 37, 51, 57, 87, 93, 102, 117, 123, 127, 135, 147, 157, 171, 177, 189, 197, 207, 219, 237, 249, 255, 261, 267, 291, 297, 303, 311, 312, 321, 327, 337, 345, 357, 363, 377, 387, 393, 397, 405, 417, 427, 447, 453, 471, 477, 483, 487, 495

Offset

1,1

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 lost positions in this game.

Links

Table of n, a(n) for n=1..54.

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, A227763.

Sequence in context: A172409 A062936 A136972 * A135115 A107402 A082618

Adjacent sequences: A227761 A227762 A227763 * A227765 A227766 A227767

Keyword

nonn

Author

José María Grau Ribas, Jul 29 2013

Status

approved