A033623 Grundy function for turn-at-most-4-coins game.

1, 2, 4, 8, 15, 16, 32, 51, 64, 85, 106, 128, 150, 171, 219, 237, 247, 256, 279, 297, 455, 512, 537, 557, 594, 643, 803, 863, 998, 1024, 1051, 1070, 1112, 1169, 1333, 1345, 1620, 1866, 2048, 2076, 2085, 2185, 2372

Offset: 1

Author

David A. Madore

Keywords

• nonn
• nice
• easy

References

• E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Table 3, page 433.

Crossrefs

Cf. A000069, A054016, A054043, etc.

Programs

Mathematica

Clear[a]; a[1] = 1; a[n_] := a[n] = (xor = BitXor @@@ Subsets[Array[a, n-1], 3] // Union ; r = Range[0, m = Last[xor]]; cp = Complement[r, xor]; If[cp == {}, m+1, First[cp]]); Table[a[n], {n, 1, 43}] (* Jean-François Alcover, Jan 09 2013 *)

Formula

a(n)=smallest natural not the exclusive-or of at most three a(k) for k

Extensions

More terms from N. J. A. Sloane Apr 29 2000

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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