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A002187
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Sprague-Grundy values for Dawson's Chess (octal game .137).
(Formerly M0025 N0007)
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10
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0, 1, 1, 2, 0, 3, 1, 1, 0, 3, 3, 2, 2, 4, 0, 5, 2, 2, 3, 3, 0, 1, 1, 3, 0, 2, 1, 1, 0, 4, 5, 2, 7, 4, 0, 1, 1, 2, 0, 3, 1, 1, 0, 3, 3, 2, 2, 4, 4, 5, 5, 2, 3, 3, 0, 1, 1, 3, 0, 2, 1, 1, 0, 4, 5, 3, 7, 4, 8, 1, 1, 2, 0, 3, 1, 1, 0, 3, 3, 2, 2, 4, 4, 5, 5, 9, 3, 3, 0, 1, 1, 3, 0, 2, 1, 1, 0, 4, 5, 3, 7, 4, 8, 1, 1, 2, 0, 3, 1, 1, 0, 3, 3, 2, 2, 4, 4, 5, 5, 9, 3, 3, 0, 1, 1, 3, 0, 2, 1, 1, 0, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Octal game .07 (Dawson's Kayles) has values a(n-1). Octal games .4, .401, .402, .403, .42, .421, .422 and .423 have values a(n-2).
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REFERENCES
| E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see pp. 89 and 102.
R. K. Guy and C. A. B. Smith, 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
| Has period 34 with the only exceptions at n=0, 14, 16, 17, 31, 34 and 51.
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PROG
| {-Haskell-}main=print(tail g); g=0:0:[mex[xor(g!!(a+1))(g!!(n-a-2))|a<-[ -1..n-2]]|n<-[1..]]; xor x y=if(x, y)==(0, 0)then 0 else let((q, r), (s, t))=(divMod x 2, divMod y 2)in(if r==t then 0 else 1)+2*xor q s; mex xs=head[x|x<-[0..], not(elem x xs)] (Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 08 2005)
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CROSSREFS
| Sequence in context: A144955 A168020 A170942 * A124756 A113504 A124754
Adjacent sequences: A002184 A002185 A002186 * A002188 A002189 A002190
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 22 2002
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