|
| |
|
|
A002187
|
|
Sprague-Grundy values for Dawson's Chess (octal game .137).
(Formerly M0025 N0007)
|
|
11
|
|
|
|
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;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
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).
|
|
|
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).
|
|
|
LINKS
|
Table of n, a(n) for n=0..131.
Achim Flammenkamp, Octal games
|
|
|
FORMULA
|
Has period 34 with the only exceptions at n=0, 14, 16, 17, 31, 34 and 51.
|
|
|
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)
|
|
|
CROSSREFS
|
Sequence in context: A225084 A209599 A170942 * A124756 A113504 A124754
Adjacent sequences: A002184 A002185 A002186 * A002188 A002189 A002190
|
|
|
KEYWORD
|
nonn,nice,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
Edited by Christian G. Bower, Oct 22 2002
|
|
|
STATUS
|
approved
|
| |
|
|
