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A180120 Positions of records of the Sprague-Grundy values of Grundy's Game. 2
0, 3, 5, 13, 18, 41, 87, 138, 158, 181, 283, 321, 541, 614, 645, 791, 939, 1016, 1056, 1291, 1349, 1393, 1399, 1535, 1742, 1882, 2035, 3029, 3032, 3197, 4019, 4985, 5006, 5441, 5744, 7091, 7384, 8337, 11261, 11621, 11885, 12037, 13133, 13146, 13679 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Tomas Rokicki, Table of n, a(n) for n = 1..82 (first 81 entries from Robert G. Wilson v)

Achim Flammenkamp, Sprague-Grundy Values of Grundy's Game

Gabriel Nivasch, The Sprague-Grundy theory of impartial games

Gabriel Nivasch, The Sprague-Grundy theory of impartial games [archived version]

MATHEMATICA

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

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];

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

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

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

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

(* Birkas Gyorgy, Apr 19 2011 *)

CROSSREFS

Cf. A002188, A180121.

Sequence in context: A084706 A002716 A046154 * A075704 A045413 A108702

Adjacent sequences:  A180117 A180118 A180119 * A180121 A180122 A180123

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 10 2010

EXTENSIONS

a(1) corrected by Tomas Rokicki, Nov 12 2020

STATUS

approved

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Last modified March 2 08:39 EST 2021. Contains 341745 sequences. (Running on oeis4.)