A126012 A106486-encoding of the canonical representative of the combinatorial game with code n.

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

Author

Antti Karttunen, Dec 18 2006

Keywords

• nonn

Examples

			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.
		

Links

• A. Karttunen, Scheme-program for computing this sequence.

Crossrefs

A126011 gives the distinct terms (and also the records).