

A071074


SpragueGrundy values for the game of Double Kayles (octal game .7777).


4



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
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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 Gvalues of various games. Proc. Cambridge Philos. Soc. 52 (1956), 514526. 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: A066990 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



