A071074 Sprague-Grundy values for the game of Double Kayles (octal game .7777).

0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 8, 9, 7, 6, 5, 4, 3, 2, 8, 9, 4, 5, 12, 13, 9, 8, 2, 3, 4, 5, 15, 14, 3, 2, 8, 9, 7, 6, 5, 4, 3, 2, 8, 9, 13, 12, 15, 14, 9, 8, 2, 3, 4, 5, 16, 17, 10, 11, 8, 9, 14, 15, 5, 4, 3, 2, 16, 17, 13, 12, 15, 14, 9, 8, 2, 3, 4, 5, 6, 7, 3, 2, 8, 9, 14, 15, 5, 4, 3, 2

Offset

0,3

Comments

Sequence is eventually periodic with period 24. The last exception is at n=141. - Eric M. Schmidt, Jan 11 2017

References

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 98.

J. H. Conway, On Numbers and Games, Second Edition. A K Peters, Ltd, 2001, p. 129.

Guy, R. K. and Smith, C. A. B.; The G-values of various games. Proc. Cambridge Philos. Soc. 52 (1956), 514-526. See page 521.

Links

Eric M. Schmidt, Table of n, a(n) for n = 0..200

Achim Flammenkamp, Octal games

Formula

Let b=A002186. Cases A, B: b(n)=0, 2, 5, 7. Cases C, D: b(n)=1, 3, 4, 6, 8. Cases A, C: n even. Cases B, D: n odd. Cases A, D: a(2n)=2*b(n), a(2n+1)=2*b(n)+1. Cases B, C: a(2n)=2*b(n)+1, a(2n+1)=2*b(n).

Crossrefs

Cf. A002186.

Sequence in context: A365296 A097449 A104415 * A279648 A066323 A245347

Adjacent sequences: A071071 A071072 A071073 * A071075 A071076 A071077

Keyword

nonn

Author

N. J. A. Sloane, May 26 2002

Extensions

Edited and extended by Christian G. Bower, Oct 22 2002

Status

approved