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Matching statistic: St001838
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Mapping
St001838: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1
1 => 1
00 => 1
01 => 3
10 => 3
11 => 1
000 => 1
001 => 4
010 => 5
011 => 4
100 => 4
101 => 5
110 => 4
111 => 1
0000 => 1
0001 => 5
0010 => 7
0011 => 6
0100 => 7
0101 => 6
0110 => 7
0111 => 5
1000 => 5
1001 => 7
1010 => 6
1011 => 7
1100 => 6
1101 => 7
1110 => 5
1111 => 1
00000 => 1
00001 => 6
00010 => 9
00011 => 8
00100 => 10
00101 => 9
00110 => 10
00111 => 8
01000 => 9
01001 => 10
01010 => 7
01011 => 9
01100 => 10
01101 => 10
01110 => 9
01111 => 6
10000 => 6
10001 => 9
10010 => 10
10011 => 10
Description
The number of nonempty primitive factors of a binary word. A word $u$ is a factor of a word $w$ if $w = p u s$ for words $p$ and $s$. A word is primitive, if it is not of the form $u^k$ for a word $u$ and an integer $k\geq 2$. Apparently, the maximal number of nonempty primitive factors a binary word of length $n$ can have is given by [[oeis:A131673]].