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A227764 Losing positions in the misere version of the Subtract-a-Prime game. 2

%I #9 May 18 2019 16:58:15

%S 2,3,11,12,27,36,37,51,57,87,93,102,117,123,127,135,147,157,171,177,

%T 189,197,207,219,237,249,255,261,267,291,297,303,311,312,321,327,337,

%U 345,357,363,377,387,393,397,405,417,427,447,453,471,477,483,487,495

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

%C 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.

%t 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[#] &]

%Y Cf. A227691, A025043, A227763.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Jul 29 2013

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)