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Positions of records of the Sprague-Grundy values of Grundy's Game.
2

%I #58 Apr 15 2024 14:58:38

%S 0,3,5,13,18,41,87,138,158,181,283,321,541,614,645,791,939,1016,1056,

%T 1291,1349,1393,1399,1535,1742,1882,2035,3029,3032,3197,4019,4985,

%U 5006,5441,5744,7091,7384,8337,11261,11621,11885,12037,13133,13146,13679

%N Positions of records of the Sprague-Grundy values of Grundy's Game.

%H Tomas Rokicki, <a href="/A180120/b180120.txt">Table of n, a(n) for n = 1..84</a> (first 81 entries from Robert G. Wilson v).

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/grundy.html"> Sprague-Grundy Values of Grundy's Game</a>

%H Gabriel Nivasch, <a href="http://www.gabrielnivasch.org/fun/combinatorial-games/sprague-grundy">The Sprague-Grundy theory of impartial games</a>

%H Gabriel Nivasch, <a href="http://web.archive.org/web/20070504194337/yucs.org/~gnivasch/cgames/spraguegrundy/index.html">The Sprague-Grundy theory of impartial games</a> [archived version]

%t mex[list_] := mex[list] = Min[Complement[Range[0, Length[list]], list]];

%t move[grundygame, list_] := move[grundygame, list] = Union@Flatten[ Union[Table[ Sort@Join[Drop[list, {i}], {list[[i]] - j, j}], {i, Length[list]}, {j, Floor[(list[[i]] - 1)/2]}], Table[Sort@Join[Drop[list, {i}], {list[[i]] - j, j}], {i, Length[list]}, {j, Ceiling[(list[[i]] + 1)/2],list[[i]] - 1}]], 1];

%t SpragueGrundy[game_, list_] := SpragueGrundy[game, list] =

%t mex[SpragueGrundy[game, #] & /@ move[game, list]];

%t sg = Table[SpragueGrundy[grundygame, {i}], {i, 42}];

%t lst = {}; a = -1; Do[If[ss[[n]] > a, a = ss[[n]]; AppendTo[lst, n]], {n, 42}]; lst

%t (* _Birkas Gyorgy_, Apr 19 2011 *)

%Y Cf. A002188, A180121.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 10 2010

%E a(1) corrected by _Tomas Rokicki_, Nov 12 2020