Identifier
- St001838: Binary words ⟶ ℤ
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
10100=>9
10101=>7
10110=>10
10111=>9
11000=>8
11001=>10
11010=>9
11011=>10
11100=>8
11101=>9
11110=>6
11111=>1
000000=>1
000001=>7
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000011=>10
000100=>13
000101=>12
000110=>13
000111=>11
001000=>13
001001=>12
001010=>11
001011=>13
001100=>14
001101=>14
001110=>13
001111=>10
010000=>11
010001=>13
010010=>12
010011=>14
010100=>11
010101=>8
010110=>13
010111=>12
011000=>13
011001=>14
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011011=>12
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011110=>11
011111=>7
100000=>7
100001=>11
100010=>13
100011=>13
100100=>12
100101=>13
100110=>14
100111=>13
101000=>12
101001=>13
101010=>8
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101101=>12
101110=>13
101111=>11
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110001=>13
110010=>14
110011=>14
110100=>13
110101=>11
110110=>12
110111=>13
111000=>11
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111011=>13
111100=>10
111101=>11
111110=>7
111111=>1
0000000=>1
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0000101=>15
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0000111=>14
0001000=>17
0001001=>16
0001010=>15
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0011000=>18
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0100111=>18
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0110000=>16
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1000000=>8
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1010100=>13
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1011101=>17
1011110=>16
1011111=>13
1100000=>12
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1100011=>18
1100100=>17
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1100110=>18
1100111=>18
1101000=>17
1101001=>18
1101010=>13
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1101110=>17
1101111=>16
1110000=>14
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1110111=>17
1111000=>14
1111001=>16
1111010=>15
1111011=>16
1111100=>12
1111101=>13
1111110=>8
1111111=>1
00000000=>1
00000001=>9
00000010=>15
00000011=>14
00000100=>19
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00000110=>19
00000111=>17
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00101100=>24
00101101=>22
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00101111=>21
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00110010=>24
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00111000=>23
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01000000=>15
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01001101=>25
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01111111=>9
10000000=>9
10000001=>15
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10000011=>19
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10001000=>20
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10111110=>19
10111111=>15
11000000=>14
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11001000=>22
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11001100=>21
11001101=>24
11001110=>23
11001111=>22
11010000=>21
11010001=>23
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11011000=>22
11011001=>23
11011010=>19
11011011=>16
11011100=>23
11011101=>20
11011110=>21
11011111=>19
11100000=>17
11100001=>21
11100010=>23
11100011=>23
11100100=>22
11100101=>23
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11100111=>23
11101000=>22
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11101010=>18
11101011=>21
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11101101=>19
11101110=>20
11101111=>21
11110000=>18
11110001=>21
11110010=>22
11110011=>22
11110100=>21
11110101=>19
11110110=>20
11110111=>21
11111000=>17
11111001=>19
11111010=>18
11111011=>19
11111100=>14
11111101=>15
11111110=>9
11111111=>1
000000000=>1
000000001=>10
000000010=>17
000000011=>16
000000100=>22
000000101=>21
000000110=>22
000000111=>20
000001000=>25
000001001=>24
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000001111=>22
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001000000=>22
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001001010=>24
001001011=>26
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001001101=>30
001001110=>29
001001111=>27
001010000=>26
001010001=>27
001010010=>25
001010011=>28
001010100=>22
001010101=>17
001010110=>26
001010111=>25
001011000=>30
001011001=>30
001011010=>27
001011011=>26
001011100=>30
001011101=>29
001011110=>28
001011111=>25
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001111000=>28
001111001=>28
001111010=>28
001111011=>28
001111100=>26
001111101=>26
001111110=>22
001111111=>16
010000000=>17
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010000010=>25
010000011=>26
010000100=>26
010000101=>27
010000110=>29
010000111=>28
010001000=>23
010001001=>25
010001010=>27
010001011=>29
010001100=>30
010001101=>31
010001110=>30
010001111=>28
010010000=>24
010010001=>25
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010010101=>24
010010110=>29
010010111=>28
010011000=>30
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010011010=>30
010011011=>30
010011100=>30
010011101=>31
010011110=>29
010011111=>26
010100000=>23
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010101000=>21
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011000100=>30
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011000110=>28
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011001010=>29
011001011=>30
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011010011=>30
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011100000=>25
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011100010=>30
011100011=>29
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011101010=>25
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011101101=>25
011101110=>23
011101111=>25
011110000=>26
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011110100=>28
011110101=>26
011110110=>26
011110111=>26
011111000=>25
011111001=>26
011111010=>25
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011111100=>22
011111101=>22
011111110=>17
011111111=>10
100000000=>10
100000001=>17
100000010=>22
100000011=>22
100000100=>25
100000101=>25
100000110=>26
100000111=>25
100001000=>26
100001001=>26
100001010=>26
100001011=>28
100001100=>28
100001101=>29
100001110=>28
100001111=>26
100010000=>25
100010001=>23
100010010=>25
100010011=>28
100010100=>27
100010101=>25
100010110=>30
100010111=>29
100011000=>28
100011001=>29
100011010=>30
100011011=>29
100011100=>29
100011101=>30
100011110=>28
100011111=>25
100100000=>24
100100001=>26
100100010=>25
100100011=>28
100100100=>18
100100101=>22
100100110=>27
100100111=>26
100101000=>27
100101001=>26
100101010=>22
100101011=>26
100101100=>30
100101101=>29
100101110=>30
100101111=>28
100110000=>28
100110001=>29
100110010=>28
100110011=>24
100110100=>30
100110101=>29
100110110=>27
100110111=>29
100111000=>29
100111001=>28
100111010=>30
100111011=>30
100111100=>28
100111101=>29
100111110=>26
100111111=>22
101000000=>21
101000001=>25
101000010=>27
101000011=>28
101000100=>26
101000101=>27
101000110=>30
101000111=>29
101001000=>25
101001001=>22
101001010=>25
101001011=>27
101001100=>30
101001101=>30
101001110=>30
101001111=>28
101010000=>23
101010001=>25
101010010=>24
101010011=>26
101010100=>17
101010101=>11
101010110=>22
101010111=>21
101011000=>28
101011001=>29
101011010=>25
101011011=>24
101011100=>28
101011101=>27
101011110=>26
101011111=>23
101100000=>26
101100001=>29
101100010=>31
101100011=>30
101100100=>30
101100101=>30
101100110=>28
101100111=>30
101101000=>28
101101001=>29
101101010=>24
101101011=>25
101101100=>23
101101101=>18
101101110=>25
101101111=>24
101110000=>28
101110001=>30
101110010=>31
101110011=>30
101110100=>29
101110101=>27
101110110=>25
101110111=>23
101111000=>28
101111001=>29
101111010=>27
101111011=>26
101111100=>26
101111101=>25
101111110=>22
101111111=>17
110000000=>16
110000001=>22
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110000011=>26
110000100=>28
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110000111=>28
110001000=>27
110001001=>28
110001010=>28
110001011=>30
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110001110=>29
110001111=>28
110010000=>27
110010001=>28
110010010=>23
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110010100=>28
110010101=>26
110010110=>30
110010111=>30
110011000=>27
110011001=>24
110011010=>30
110011011=>29
110011100=>28
110011101=>30
110011110=>28
110011111=>26
110100000=>25
110100001=>28
110100010=>29
110100011=>30
110100100=>26
110100101=>27
110100110=>30
110100111=>30
110101000=>25
110101001=>26
110101010=>17
110101011=>22
110101100=>28
110101101=>25
110101110=>27
110101111=>26
110110000=>27
110110001=>29
110110010=>30
110110011=>29
110110100=>26
110110101=>24
110110110=>18
110110111=>22
110111000=>29
110111001=>30
110111010=>26
110111011=>23
110111100=>28
110111101=>26
110111110=>25
110111111=>22
111000000=>20
111000001=>25
111000010=>28
111000011=>28
111000100=>29
111000101=>29
111000110=>29
111000111=>29
111001000=>28
111001001=>26
111001010=>28
111001011=>30
111001100=>27
111001101=>30
111001110=>28
111001111=>28
111010000=>27
111010001=>29
111010010=>28
111010011=>30
111010100=>25
111010101=>21
111010110=>27
111010111=>27
111011000=>28
111011001=>29
111011010=>25
111011011=>22
111011100=>27
111011101=>23
111011110=>26
111011111=>25
111100000=>22
111100001=>26
111100010=>28
111100011=>28
111100100=>27
111100101=>28
111100110=>28
111100111=>28
111101000=>27
111101001=>28
111101010=>23
111101011=>26
111101100=>27
111101101=>24
111101110=>25
111101111=>26
111110000=>22
111110001=>25
111110010=>26
111110011=>26
111110100=>25
111110101=>23
111110110=>24
111110111=>25
111111000=>20
111111001=>22
111111010=>21
111111011=>22
111111100=>16
111111101=>17
111111110=>10
111111111=>1
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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.
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.
Code
def statistic(w): return sum(1 for f in w.factor_iterator() if f and f.is_primitive())
Created
Sep 16, 2022 at 10:06 by Martin Rubey
Updated
Sep 16, 2022 at 10:06 by Martin Rubey
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