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A106486-encodings of combinatorial games with value 1.
1

%I #4 Mar 31 2012 13:21:13

%S 1,17,65,81,513,529,577,593,2049,2065,2113,2129,2561,2577,2625,2641,

%T 4097,4113,4161,4177,4609,4625,4673,4689,6145,6161,6209,6225,6657,

%U 6673,6721,6737,8193,8209,8257,8273,8705,8721,8769,8785,10241,10257

%N A106486-encodings of combinatorial games with value 1.

%C These are codes for games which belong to the same equivalence class as the game {0|} (i.e. game 1).

%H A. Karttunen, <a href="/A126000/a126000.scm.txt">Scheme-program for computing this sequence.</a>

%e Game {0|} is encoded as 2^(2*0) = 1, thus 1 is the first term of this sequence. Also 17 belongs into this sequence, as it encodes game {-1,0|}, where, as the option -1 is dominated by option 0, the former can be deleted, resulting the same game {0|}. Also code 65536 (= 2^(2*(2^(1+2*1)))) belongs into this sequence, as it encodes the game {{|1}|}, which is reversible to game 1.

%Y Row 2 of A126000.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 18 2006