A180120 Indices of record high-points in the sequence of Sprague-Grundy values for 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[sg[[n]] > a, a = sg[[n]]; AppendTo[lst, n]], {n, 42}]; lst
(* Birkas Gyorgy, Apr 19 2011 *)
A002188 =  Cases[Import["https://oeis.org/A002188/b002188.txt",
   "Table"], {_, _}][[All, 2]];
lg = Length[A002188];
A180120 = {};
a = -1;
Do[If[A002188[[n]] > a, a = A002188[[n]]; AppendTo[A180120, n - 1]], {n, lg}];
A180120
(* Robert Price, Mar 23 2025 *)

Crossrefs

Cf. A002188, A180121.

Sequence in context: A393152 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

Definition edited by N. J. A. Sloane, Mar 22 2025

Status

approved