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A227691
Winning positions in the Subtract-a-Prime game.
4
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved