A126003 -id:A126003 - cp's OEIS frontend

A126001 A106486-encodings of nonnegative combinatorial games, i.e., games whose value is >= 0.

0, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 128, 129, 132, 133, 136, 137, 140, 141, 144, 145, 148, 149, 152, 153, 156, 157, 192, 193, 196, 197, 200, 201, 204, 205, 208, 209, 212, 213, 216

Offset: 1

Antti Karttunen, Dec 18 2006

nonn

In these games, the left can always win if he is to play second.

Antti Karttunen, Table of n, a(n) for n = 1..16386
A. Karttunen, Scheme-program for computing this sequence.

Characteristic function (A320006) occurs as row 0 of A125999.

Cf. A125991, A126003, A126004, A126005.

A320006(n) = if(!n,1,my(m=(n>>1), r=0); while(m>0, if((m%2)&&!A320007(r),return(0)); m >>= 2; r++); (1));
A320007(n) = if(!n,0,my(m=n, s=0); while(m>0, if((m%2)&&A320006(s),return(1)); m >>= 2; s++); (0));
k=0; n=0; while(k<16386, if(A320006(n), k++; write("b126001.txt", k, " ", n)); n++);

A126002 A106486-encodings of combinatorial games whose value is <= 0.

Original entry on oeis.org

0, 2, 8, 10, 16, 18, 24, 26, 32, 34, 40, 42, 48, 50, 56, 58, 64, 66, 72, 74, 80, 82, 88, 90, 96, 98, 104, 106, 112, 114, 120, 122, 128, 130, 136, 138, 144, 146, 152, 154, 160, 162, 168, 170, 176, 178, 184, 186, 192, 194, 200, 202, 208, 210, 216, 218, 224, 226, 232, 234, 240, 242, 248, 250, 512, 514

Offset: 1

Antti Karttunen, Dec 18 2006

nonn

In these games, the right can always win if he is to play second.

Antti Karttunen, Table of n, a(n) for n = 1..16384
A. Karttunen, Scheme-program for computing this sequence.
Index entries for sequences which agree for a long time but are different

Characteristic function occurs as column 0 of A125999. Differs from A047467 (a(65)=512, not 256) and also from A079599, as the term 18446744073709551616 (= 2^64) is a member of this sequence but not of A079599. Cf. A125991, A126003-A126005.

A126005 A106486-encodings of combinatorial games whose value is less than zero.

Original entry on oeis.org

2, 10, 18, 26, 32, 34, 40, 42, 48, 50, 56, 58, 66, 74, 82, 90, 96, 98, 104, 106, 112, 114, 120, 122, 130, 138, 146, 154, 160, 162, 168, 170, 176, 178, 184, 186, 194, 202, 210, 218, 224, 226, 232, 234, 240, 242, 248, 250, 514, 522, 530, 538, 544, 546, 552, 554

Offset: 1

Antti Karttunen, Dec 18 2006

nonn

In these games, the right can always win.

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

Intersection of complement of A126001 and A126002. Cf. A125991, A126001-A126003.

A125994 A106486-encodings of combinatorial games equivalent to game {0|0}.

Original entry on oeis.org

3, 11, 19, 27, 515, 523, 531, 539, 2051, 2059, 2067, 2075, 2563, 2571, 2579, 2587, 8195, 8203, 8211, 8219, 8707, 8715, 8723, 8731, 10243, 10251, 10259, 10267, 10755, 10763, 10771, 10779, 32771, 32779, 32787, 32795, 33283, 33291, 33299

Offset: 1

Antti Karttunen, Dec 18 2006

nonn

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

			Game {0|0} is encoded as 2^(2*0) + 2^(1+2*0) = 3, thus 3 is the first term of this sequence. However, 11 also belongs into this sequence, as it encodes game {0|0,1}, where, because the option 0 dominates the option 1 on the right hand side, the latter can be deleted, resulting the same game {0|0}.

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

Row 4 of A126000. Subset of A126003.

A126004 A106486-encodings of combinatorial games whose value is greater than zero.

Original entry on oeis.org

1, 4, 5, 9, 12, 13, 17, 20, 21, 25, 28, 29, 65, 68, 69, 73, 76, 77, 81, 84, 85, 89, 92, 93, 129, 132, 133, 137, 140, 141, 145, 148, 149, 153, 156, 157, 193, 196, 197, 201, 204, 205, 209, 212, 213, 217, 220, 221, 256, 257, 260, 261, 264, 265, 268, 269, 272, 273

Offset: 1

Antti Karttunen, Dec 18 2006

nonn

In these games, the left can always win.

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

Intersection of complement of A126002 and A126001. Cf. A125991, A126001-A126003.

cp's OEIS Frontend

A126001 A106486-encodings of nonnegative combinatorial games, i.e., games whose value is >= 0.

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A126002 A106486-encodings of combinatorial games whose value is <= 0.

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A126005 A106486-encodings of combinatorial games whose value is less than zero.

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A125994 A106486-encodings of combinatorial games equivalent to game {0|0}.

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A126004 A106486-encodings of combinatorial games whose value is greater than zero.

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