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A126011 A106486-encodings for the minimal representatives of each equivalence class of the finite combinatorial games. 7
0, 1, 2, 3, 4, 6, 9, 12, 18, 32, 33, 36, 48, 66, 67, 96, 97, 129, 131, 132, 134, 195, 256, 258, 264, 288, 384, 386, 516, 768, 4098, 4099, 4102, 4128, 4129, 4132, 4227, 4230, 8196, 8198, 8204, 8448, 8450, 8456, 12294, 262146, 262152, 262176, 262272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The initial terms correspond with the following games: code 0 = {|} = the zero game, code 1 = {0|} = game 1, code 2 = {|0} = game -1, code 3 = {0|0} = game *, code 4 = {1|} = game 2, code 6 = {1|0}, code 9 = {0|1} = game 1/2, code 12 = {1|1} = game 1*, code 18 = {-1|0} = game -1/2, code 32 = {|-1} = game -2, code 33 = {0|-1}, code 36 = {1|-1} = game +-1, code 48 = {-1|-1} = game -1*, code 66 = {*|0} = game down, code 67 = {0,*|0} = game up*, code 96 = {*|-1}, code 97 = {0,*|-1}, code 129 = {0|*} = game up, code 131 = {0|0,*} = game down*, code 132 = {1|*}, code 134 = {1|0,*}, code 195 = {0,*|0,*} = game *2, code 256 = {2|} = game 3. Encoding is explained in A106486.

REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Second Edition, Vol. 1, A K Peters, 2001.

John H. Conway, On Numbers and Games, Second Edition, A K Peters, 2001.

LINKS

A. Karttunen, Table of n, a(n) for n = 0..73

D. Eppstein, Combinatorial Game Theory links

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

A. Siegel, Combinatorial Game Suite

Wikipedia, Combinatorial game theory

D. Wolfe, Several publications about combinatorial game theory

CROSSREFS

Records in A126012. Column 1 of A126000. Inverse: A126013. See also A126009 & A126010. A125990 gives the number of terms in range [0, 2^n[.

Sequences A034797, A034798, A079599 utilize a similar encoding system for impartial games.

Sequence in context: A017823 A017982 A139076 * A018256 A111791 A178479

Adjacent sequences:  A126008 A126009 A126010 * A126012 A126013 A126014

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 18 2006

EXTENSIONS

Table of terms added Jan 01 2007.

STATUS

approved

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Last modified December 13 09:55 EST 2017. Contains 295957 sequences.