AUTHOR
_Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), _, Dec 18 2006
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Revision History for A126012
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A106486-encoding of the canonical representative of the combinatorial game with code n.
(history; published version)
(history; published version)
LINKS
A. Karttunen, <a href="/A126000/a126000.scm.txt">Scheme-program for computing this sequence.</a>
KEYWORD
nonn,new
nonn
LINKS
A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/a126000.scm.txt">Scheme-program for computing this sequence.</a>
KEYWORD
nonn,new
nonn
NAME
A106486-encoding of the canonical representative of the combinatorial game with code n.
DATA
0, 1, 2, 3, 4, 4, 6, 6, 0, 9, 2, 3, 12, 12, 6, 6, 0, 1, 18, 3, 4, 4, 6, 6, 0, 9, 18, 3, 12, 12, 6, 6, 32, 33, 32, 33, 36, 36, 36, 36, 32, 33, 32, 33, 36, 36, 36, 36, 48, 33, 48, 33, 36, 36, 36, 36, 48, 33, 48, 33, 36, 36, 36, 36, 0, 1, 66, 67, 4, 4, 6, 6, 0, 9, 66, 67, 12, 12, 6, 6
OFFSET
0,3
LINKS
A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/a126000.scm.txt">Scheme-program for computing this sequence.</a>
EXAMPLE
25 (= 2^(2*2) + 2^(2*0) + 2^(1+2*1)) encodes the game {-1,0|1}, where, as the option -1 is dominated by option 0, the former can be deleted, giving us the game {0|1}, i.e. the canonical (minimal) form of the game 1/2, encoded as 2^(2*0) + 2^(1+2*1) = 9, thus a(25)=9 and a(9)=9. Similarly a(65536)=1, as 65536 (= 2^(2*(2^(1+2*1)))) encodes the game {{|1}|}, which is reversible to the game {0|}, i.e. the game 1, which is encoded as 2^(2*0) = 1.
CROSSREFS
A126011 gives the distinct terms (and also the records).
KEYWORD
nonn
AUTHOR
Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 18 2006
STATUS
approved