A126005 -id:A126005 - 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.

A126003 A106486-encodings of combinatorial games whose value is incomparable with zero game, i.e., fuzzy games.

Original entry on oeis.org

3, 6, 7, 11, 14, 15, 19, 22, 23, 27, 30, 31, 33, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 67, 70, 71, 75, 78, 79, 83, 86, 87, 91, 94, 95, 97, 99, 100, 101, 102, 103, 105, 107, 108, 109, 110, 111, 113, 115, 116, 117, 118

Offset: 1

Antti Karttunen, Dec 18 2006

nonn

In these games, the first player can always win.

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

Intersection of the complements of A126001 and A126002, or equally, complement of the union of A126001 and A126002. Differs from A047556. Cf. A125991, A125994, A126004-A126005.

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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A126003 A106486-encodings of combinatorial games whose value is incomparable with zero game, i.e., fuzzy games.

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