A227691 Winning positions in the Subtract-a-Prime game.

2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

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 loses. This sequence is the set of winner positions in this game.

Complement of A025043.

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, False, ! Select[moves[n], !gana[#] &] == {}];
Select[Range[155], gana[#] &]

Prog

(PARI) is(n)=if(isprime(n) || isprime(n-1), return(1)); if(n<15, return(0)); for(k=9, n-1, if(isprime(n-k) && !is(k), return(1))); 0 \\ Charles R Greathouse IV, Nov 13 2013

Crossrefs

The Grundy numbers of this game are in A014589.

Sequence in context: A265573 A265557 A162343 * A167703 A039272 A039209

Adjacent sequences: A227688 A227689 A227690 * A227692 A227693 A227694

Keyword

nonn

Author

José María Grau Ribas, Jul 19 2013

Status

approved