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Matching statistic: St000682
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Mapping
St000682: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 0
01 => 1
10 => 0
11 => 0
000 => 0
001 => 2
010 => 1
011 => 2
100 => 0
101 => 1
110 => 0
111 => 0
0000 => 0
0001 => 3
0010 => 2
0011 => 0
0100 => 1
0101 => 1
0110 => 2
0111 => 3
1000 => 0
1001 => 2
1010 => 1
1011 => 2
1100 => 0
1101 => 1
1110 => 0
1111 => 0
00000 => 0
00001 => 4
00010 => 3
00011 => 6
00100 => 2
00101 => 5
00110 => 0
00111 => 6
01000 => 1
01001 => 4
01010 => 1
01011 => 5
01100 => 2
01101 => 4
01110 => 3
01111 => 4
10000 => 0
10001 => 3
10010 => 2
10011 => 0
Description
The Grundy value of Welter's game on a binary word. Two players take turns moving a $1$ to the left. The loosing positions are the words $1\dots 10\dots 0$.