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Nim value of subtraction game S(2,5,7) with a heap of n beans.
0

%I #15 Sep 08 2022 08:46:15

%S 0,0,1,1,0,2,1,3,2,2,0,3,1,0,0,1,1,2,2,3,3,2,0,0,1,1,0,2,1,3,2,2,0,3,

%T 1,0,0,1,1,2,2,3,3,2,0,0,1,1,0,2,1,3,2,2,0,3,1,0,0,1,1,2,2,3,3,2,0,0,

%U 1,1,0,2,1,3,2,2,0,3,1,0,0,1,1,2,2,3,3,2,0,0,1,1,0,2,1,3,2,2,0,3,1,0,0,1,1,2,2,3,3,2,0,0,1,1,0,2,1,3,2,2,0,3,1,0,0,1,1,2,2,3,3,2

%N Nim value of subtraction game S(2,5,7) with a heap of n beans.

%C Periodic with period-length 22: repeat {0, 0, 1, 1, 0, 2, 1, 3, 2, 2, 0, 3, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2}.

%D R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 38.

%t PadRight[{}, 120, {0, 0, 1, 1, 0, 2, 1, 3, 2, 2, 0, 3, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2}] (* _Vincenzo Librandi_, Jan 11 2016 *)

%o (Magma) &cat[[0,0,1,1,0,2,1,3,2,2,0,3,1,0,0,1,1,2,2,3,3,2]^^5]; // _Vincenzo Librandi_, Jan 11 2016

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_, Jan 03 2016