Search: id:A002186
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%I A002186 M0410 N0156
%S A002186 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,
%T A002186 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,
%U A002186 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
%N A002186 Sprague-Grundy values for the game of Kayles (octal games .77 and .771).
%C A002186 Octal games 4.4, 4.41, 4.42, 4.43, 4.6, 4.61, 4.62 and 4.63 have values 
               a(n-1).
%C A002186 "The periodicity was first proved by R. K. Guy in 1949, the sequence 
               necessarily being calculated by hand." [Beasley].
%D A002186 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002186 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002186 E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, 
               NY, 2 vols., 1982, see p. 91.
%D A002186 J. H. Conway, On Numbers and Games, Second Edition. A K Peters, Ltd, 
               2001, p. 128.
%D A002186 Guy, R. K. and Smith, C. A. B.; The G-values of various games. Proc. 
               Cambridge Philos. Soc. 52 (1956), 514-526.
%D A002186 John D. Beasley, The Mathematics of Games, Dover Publ., Mineola, NY 2006, 
               page 111.
%H A002186 Achim Flammenkamp, <a href="http://www.uni-bielefeld.de/~achim/octal_sparse.html">
               Octal games</a>
%F A002186 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.
%Y A002186 Cf. A071074, A071434.
%Y A002186 Sequence in context: A125933 A011857 A006021 this_sequence A125936 A161621 
               A095701
%Y A002186 Adjacent sequences: A002183 A002184 A002185 this_sequence A002187 A002188 
               A002189
%K A002186 nonn,nice
%O A002186 0,3
%A A002186 N. J. A. Sloane (njas(AT)research.att.com).
%E A002186 More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), 
               Dec 08 2001
%E A002186 Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 22 2002

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