A180120 Positions of records of the Sprague-Grundy values of Grundy's Game.

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

Offset

1,2

Links

Tomas Rokicki, Table of n, a(n) for n = 1..84 (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 * A377318 A075704 A045413

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