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A002186
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Sprague-Grundy values for the game of Kayles (octal games .77 and .771).
(Formerly M0410 N0156)
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3
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0, 1, 2, 3, 1, 4, 3, 2, 1, 4, 2, 6, 4, 1, 2, 7, 1, 4, 3, 2, 1, 4, 6, 7, 4, 1, 2, 8, 5, 4, 7, 2, 1, 8, 6, 7, 4, 1, 2, 3, 1, 4, 7, 2, 1, 8, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 4, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 6, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Octal games 4.4, 4.41, 4.42, 4.43, 4.6, 4.61, 4.62 and 4.63 have values a(n-1).
"The periodicity was first proved by R. K. Guy in 1949, the sequence necessarily being calculated by hand." [Beasley].
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REFERENCES
| John D. Beasley, The Mathematics of Games, Dover Publ., Mineola, NY 2006, page 111.
E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 91.
Calkin, Neil J.; James, Kevin; Janoski, Janine E.; Leggett, Sarah; Richards, Bryce; Sitaraman, Nathan; and Thomas, Stephanie M.; Computing strategies for graphical Nim, in Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 171-185. (See page 174.)
J. H. Conway, On Numbers and Games, Second Edition. A K Peters, Ltd, 2001, p. 128.
Guy, R. K. and Smith, C. A. B.; The G-values of various games. Proc. Cambridge Philos. Soc. 52 (1956), 514-526.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Achim Flammenkamp, Octal games
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FORMULA
| From n=71 on, the sequence is periodic with period 12. The only exceptions are n=0, 3, 6, 9, 11, 15, 18, 21, 22, 28, 34, 39, 57 and 70.
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CROSSREFS
| Cf. A071074, A071434.
Sequence in context: A125933 A011857 A006021 * A125936 A200942 A161621
Adjacent sequences: A002183 A002184 A002185 * A002187 A002188 A002189
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 08 2001
Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 22 2002
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