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

Author

N. J. A. Sloane, May 26 2002

Keywords

• nonn

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

Crossrefs

Cf. A002186.

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).

Extensions

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