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

1,2

References

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

Links

Table of n, a(n) for n=1..43.

Formula

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

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 *)

Crossrefs

Cf. A000069, A054016, A054043, etc.

Sequence in context: A328677 A039743 A070008 * A094398 A277728 A287163

Adjacent sequences: A033620 A033621 A033622 * A033624 A033625 A033626

Keyword

nonn,nice,easy

Author

David A. Madore

Extensions

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

Status

approved