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Identifier
Values
=>
0=>1 1=>1 00=>1 01=>2 10=>2 11=>1 000=>1 001=>3 010=>2 011=>3 100=>3 101=>2 110=>3 111=>1 0000=>1 0001=>4 0010=>3 0011=>4 0100=>3 0101=>2 0110=>3 0111=>4 1000=>4 1001=>3 1010=>2 1011=>3 1100=>4 1101=>3 1110=>4 1111=>1 00000=>1 00001=>5 00010=>4 00011=>5 00100=>3 00101=>5 00110=>4 00111=>5 01000=>4 01001=>3 01010=>2 01011=>5 01100=>4 01101=>3 01110=>4 01111=>5 10000=>5 10001=>4 10010=>3 10011=>4 10100=>5 10101=>2 10110=>3 10111=>4 11000=>5 11001=>4 11010=>5 11011=>3 11100=>5 11101=>4 11110=>5 11111=>1 000000=>1 000001=>6 000010=>5 000011=>6 000100=>4 000101=>6 000110=>5 000111=>6 001000=>4 001001=>3 001010=>5 001011=>6 001100=>4 001101=>6 001110=>5 001111=>6 010000=>5 010001=>4 010010=>3 010011=>6 010100=>5 010101=>2 010110=>5 010111=>6 011000=>5 011001=>4 011010=>5 011011=>3 011100=>5 011101=>4 011110=>5 011111=>6 100000=>6 100001=>5 100010=>4 100011=>5 100100=>3 100101=>5 100110=>4 100111=>5 101000=>6 101001=>5 101010=>2 101011=>5 101100=>6 101101=>3 101110=>4 101111=>5 110000=>6 110001=>5 110010=>6 110011=>4 110100=>6 110101=>5 110110=>3 110111=>4 111000=>6 111001=>5 111010=>6 111011=>4 111100=>6 111101=>5 111110=>6 111111=>1 0000000=>1 0000001=>7 0000010=>6 0000011=>7 0000100=>5 0000101=>7 0000110=>6 0000111=>7 0001000=>4 0001001=>7 0001010=>6 0001011=>7 0001100=>5 0001101=>7 0001110=>6 0001111=>7 0010000=>5 0010001=>4 0010010=>3 0010011=>7 0010100=>5 0010101=>7 0010110=>6 0010111=>7 0011000=>5 0011001=>4 0011010=>6 0011011=>7 0011100=>5 0011101=>7 0011110=>6 0011111=>7 0100000=>6 0100001=>5 0100010=>4 0100011=>7 0100100=>3 0100101=>5 0100110=>6 0100111=>7 0101000=>6 0101001=>5 0101010=>2 0101011=>7 0101100=>6 0101101=>5 0101110=>6 0101111=>7 0110000=>6 0110001=>5 0110010=>6 0110011=>4 0110100=>6 0110101=>5 0110110=>3 0110111=>7 0111000=>6 0111001=>5 0111010=>6 0111011=>4 0111100=>6 0111101=>5 0111110=>6 0111111=>7 1000000=>7 1000001=>6 1000010=>5 1000011=>6 1000100=>4 1000101=>6 1000110=>5 1000111=>6 1001000=>7 1001001=>3 1001010=>5 1001011=>6 1001100=>4 1001101=>6 1001110=>5 1001111=>6 1010000=>7 1010001=>6 1010010=>5 1010011=>6 1010100=>7 1010101=>2 1010110=>5 1010111=>6 1011000=>7 1011001=>6 1011010=>5 1011011=>3 1011100=>7 1011101=>4 1011110=>5 1011111=>6 1100000=>7 1100001=>6 1100010=>7 1100011=>5 1100100=>7 1100101=>6 1100110=>4 1100111=>5 1101000=>7 1101001=>6 1101010=>7 1101011=>5 1101100=>7 1101101=>3 1101110=>4 1101111=>5 1110000=>7 1110001=>6 1110010=>7 1110011=>5 1110100=>7 1110101=>6 1110110=>7 1110111=>4 1111000=>7 1111001=>6 1111010=>7 1111011=>5 1111100=>7 1111101=>6 1111110=>7 1111111=>1 00000000=>1 00000001=>8 00000010=>7 00000011=>8 00000100=>6 00000101=>8 00000110=>7 00000111=>8 00001000=>5 00001001=>8 00001010=>7 00001011=>8 00001100=>6 00001101=>8 00001110=>7 00001111=>8 00010000=>5 00010001=>4 00010010=>7 00010011=>8 00010100=>6 00010101=>8 00010110=>7 00010111=>8 00011000=>5 00011001=>8 00011010=>7 00011011=>8 00011100=>6 00011101=>8 00011110=>7 00011111=>8 00100000=>6 00100001=>5 00100010=>4 00100011=>8 00100100=>3 00100101=>8 00100110=>7 00100111=>8 00101000=>6 00101001=>5 00101010=>7 00101011=>8 00101100=>6 00101101=>8 00101110=>7 00101111=>8 00110000=>6 00110001=>5 00110010=>7 00110011=>4 00110100=>6 00110101=>8 00110110=>7 00110111=>8 00111000=>6 00111001=>5 00111010=>7 00111011=>8 00111100=>6 00111101=>8 00111110=>7 00111111=>8 01000000=>7 01000001=>6 01000010=>5 01000011=>8 01000100=>4 01000101=>6 01000110=>7 01000111=>8 01001000=>7 01001001=>3 01001010=>5 01001011=>8 01001100=>7 01001101=>6 01001110=>7 01001111=>8 01010000=>7 01010001=>6 01010010=>5 01010011=>8 01010100=>7 01010101=>2 01010110=>7 01010111=>8 01011000=>7 01011001=>6 01011010=>5 01011011=>8 01011100=>7 01011101=>6 01011110=>7 01011111=>8 01100000=>7 01100001=>6 01100010=>7 01100011=>5 01100100=>7 01100101=>6 01100110=>4 01100111=>8 01101000=>7 01101001=>6 01101010=>7 01101011=>5 01101100=>7 01101101=>3 01101110=>7 01101111=>8 01110000=>7 01110001=>6 01110010=>7 01110011=>5 01110100=>7 01110101=>6 01110110=>7 01110111=>4 01111000=>7 01111001=>6 01111010=>7 01111011=>5 01111100=>7 01111101=>6 01111110=>7 01111111=>8 10000000=>8 10000001=>7 10000010=>6 10000011=>7 10000100=>5 10000101=>7 10000110=>6 10000111=>7 10001000=>4 10001001=>7 10001010=>6 10001011=>7 10001100=>5 10001101=>7 10001110=>6 10001111=>7 10010000=>8 10010001=>7 10010010=>3 10010011=>7 10010100=>5 10010101=>7 10010110=>6 10010111=>7 10011000=>8 10011001=>4 10011010=>6 10011011=>7 10011100=>5 10011101=>7 10011110=>6 10011111=>7 10100000=>8 10100001=>7 10100010=>6 10100011=>7 10100100=>8 10100101=>5 10100110=>6 10100111=>7 10101000=>8 10101001=>7 10101010=>2 10101011=>7 10101100=>8 10101101=>5 10101110=>6 10101111=>7 10110000=>8 10110001=>7 10110010=>6 10110011=>7 10110100=>8 10110101=>5 10110110=>3 10110111=>7 10111000=>8 10111001=>7 10111010=>6 10111011=>4 10111100=>8 10111101=>5 10111110=>6 10111111=>7 11000000=>8 11000001=>7 11000010=>8 11000011=>6 11000100=>8 11000101=>7 11000110=>5 11000111=>6 11001000=>8 11001001=>7 11001010=>8 11001011=>6 11001100=>4 11001101=>7 11001110=>5 11001111=>6 11010000=>8 11010001=>7 11010010=>8 11010011=>6 11010100=>8 11010101=>7 11010110=>5 11010111=>6 11011000=>8 11011001=>7 11011010=>8 11011011=>3 11011100=>8 11011101=>4 11011110=>5 11011111=>6 11100000=>8 11100001=>7 11100010=>8 11100011=>6 11100100=>8 11100101=>7 11100110=>8 11100111=>5 11101000=>8 11101001=>7 11101010=>8 11101011=>6 11101100=>8 11101101=>7 11101110=>4 11101111=>5 11110000=>8 11110001=>7 11110010=>8 11110011=>6 11110100=>8 11110101=>7 11110110=>8 11110111=>5 11111000=>8 11111001=>7 11111010=>8 11111011=>6 11111100=>8 11111101=>7 11111110=>8 11111111=>1 000000000=>1 000000001=>9 000000010=>8 000000011=>9 000000100=>7 000000101=>9 000000110=>8 000000111=>9 000001000=>6 000001001=>9 000001010=>8 000001011=>9 000001100=>7 000001101=>9 000001110=>8 000001111=>9 000010000=>5 000010001=>9 000010010=>8 000010011=>9 000010100=>7 000010101=>9 000010110=>8 000010111=>9 000011000=>6 000011001=>9 000011010=>8 000011011=>9 000011100=>7 000011101=>9 000011110=>8 000011111=>9 000100000=>6 000100001=>5 000100010=>4 000100011=>9 000100100=>7 000100101=>9 000100110=>8 000100111=>9 000101000=>6 000101001=>9 000101010=>8 000101011=>9 000101100=>7 000101101=>9 000101110=>8 000101111=>9 000110000=>6 000110001=>5 000110010=>8 000110011=>9 000110100=>7 000110101=>9 000110110=>8 000110111=>9 000111000=>6 000111001=>9 000111010=>8 000111011=>9 000111100=>7 000111101=>9 000111110=>8 000111111=>9 001000000=>7 001000001=>6 001000010=>5 001000011=>9 001000100=>4 001000101=>9 001000110=>8 001000111=>9 001001000=>7 001001001=>3 001001010=>8 001001011=>9 001001100=>7 001001101=>9 001001110=>8 001001111=>9 001010000=>7 001010001=>6 001010010=>5 001010011=>9 001010100=>7 001010101=>9 001010110=>8 001010111=>9 001011000=>7 001011001=>6 001011010=>8 001011011=>9 001011100=>7 001011101=>9 001011110=>8 001011111=>9 001100000=>7 001100001=>6 001100010=>8 001100011=>5 001100100=>7 001100101=>9 001100110=>4 001100111=>9 001101000=>7 001101001=>6 001101010=>8 001101011=>9 001101100=>7 001101101=>9 001101110=>8 001101111=>9 001110000=>7 001110001=>6 001110010=>8 001110011=>5 001110100=>7 001110101=>9 001110110=>8 001110111=>9 001111000=>7 001111001=>6 001111010=>8 001111011=>9 001111100=>7 001111101=>9 001111110=>8 001111111=>9 010000000=>8 010000001=>7 010000010=>6 010000011=>9 010000100=>5 010000101=>7 010000110=>8 010000111=>9 010001000=>4 010001001=>7 010001010=>6 010001011=>9 010001100=>8 010001101=>7 010001110=>8 010001111=>9 010010000=>8 010010001=>7 010010010=>3 010010011=>9 010010100=>5 010010101=>7 010010110=>8 010010111=>9 010011000=>8 010011001=>7 010011010=>6 010011011=>9 010011100=>8 010011101=>7 010011110=>8 010011111=>9 010100000=>8 010100001=>7 010100010=>6 010100011=>9 010100100=>8 010100101=>5 010100110=>8 010100111=>9 010101000=>8 010101001=>7 010101010=>2 010101011=>9 010101100=>8 010101101=>7 010101110=>8 010101111=>9 010110000=>8 010110001=>7 010110010=>6 010110011=>9 010110100=>8 010110101=>5 010110110=>8 010110111=>9 010111000=>8 010111001=>7 010111010=>6 010111011=>9 010111100=>8 010111101=>7 010111110=>8 010111111=>9 011000000=>8 011000001=>7 011000010=>8 011000011=>6 011000100=>8 011000101=>7 011000110=>5 011000111=>9 011001000=>8 011001001=>7 011001010=>8 011001011=>6 011001100=>4 011001101=>7 011001110=>8 011001111=>9 011010000=>8 011010001=>7 011010010=>8 011010011=>6 011010100=>8 011010101=>7 011010110=>5 011010111=>9 011011000=>8 011011001=>7 011011010=>8 011011011=>3 011011100=>8 011011101=>7 011011110=>8 011011111=>9 011100000=>8 011100001=>7 011100010=>8 011100011=>6 011100100=>8 011100101=>7 011100110=>8 011100111=>5 011101000=>8 011101001=>7 011101010=>8 011101011=>6 011101100=>8 011101101=>7 011101110=>4 011101111=>9 011110000=>8 011110001=>7 011110010=>8 011110011=>6 011110100=>8 011110101=>7 011110110=>8 011110111=>5 011111000=>8 011111001=>7 011111010=>8 011111011=>6 011111100=>8 011111101=>7 011111110=>8 011111111=>9 100000000=>9 100000001=>8 100000010=>7 100000011=>8 100000100=>6 100000101=>8 100000110=>7 100000111=>8 100001000=>5 100001001=>8 100001010=>7 100001011=>8 100001100=>6 100001101=>8 100001110=>7 100001111=>8 100010000=>9 100010001=>4 100010010=>7 100010011=>8 100010100=>6 100010101=>8 100010110=>7 100010111=>8 100011000=>5 100011001=>8 100011010=>7 100011011=>8 100011100=>6 100011101=>8 100011110=>7 100011111=>8 100100000=>9 100100001=>8 100100010=>7 100100011=>8 100100100=>3 100100101=>8 100100110=>7 100100111=>8 100101000=>9 100101001=>5 100101010=>7 100101011=>8 100101100=>6 100101101=>8 100101110=>7 100101111=>8 100110000=>9 100110001=>8 100110010=>7 100110011=>4 100110100=>6 100110101=>8 100110110=>7 100110111=>8 100111000=>9 100111001=>5 100111010=>7 100111011=>8 100111100=>6 100111101=>8 100111110=>7 100111111=>8 101000000=>9 101000001=>8 101000010=>7 101000011=>8 101000100=>9 101000101=>6 101000110=>7 101000111=>8 101001000=>9 101001001=>8 101001010=>5 101001011=>8 101001100=>9 101001101=>6 101001110=>7 101001111=>8 101010000=>9 101010001=>8 101010010=>7 101010011=>8 101010100=>9 101010101=>2 101010110=>7 101010111=>8 101011000=>9 101011001=>8 101011010=>5 101011011=>8 101011100=>9 101011101=>6 101011110=>7 101011111=>8 101100000=>9 101100001=>8 101100010=>7 101100011=>8 101100100=>9 101100101=>6 101100110=>7 101100111=>8 101101000=>9 101101001=>8 101101010=>7 101101011=>5 101101100=>9 101101101=>3 101101110=>7 101101111=>8 101110000=>9 101110001=>8 101110010=>7 101110011=>8 101110100=>9 101110101=>6 101110110=>7 101110111=>4 101111000=>9 101111001=>8 101111010=>7 101111011=>5 101111100=>9 101111101=>6 101111110=>7 101111111=>8 110000000=>9 110000001=>8 110000010=>9 110000011=>7 110000100=>9 110000101=>8 110000110=>6 110000111=>7 110001000=>9 110001001=>8 110001010=>9 110001011=>7 110001100=>5 110001101=>8 110001110=>6 110001111=>7 110010000=>9 110010001=>8 110010010=>9 110010011=>7 110010100=>9 110010101=>8 110010110=>6 110010111=>7 110011000=>9 110011001=>4 110011010=>9 110011011=>7 110011100=>5 110011101=>8 110011110=>6 110011111=>7 110100000=>9 110100001=>8 110100010=>9 110100011=>7 110100100=>9 110100101=>8 110100110=>6 110100111=>7 110101000=>9 110101001=>8 110101010=>9 110101011=>7 110101100=>9 110101101=>5 110101110=>6 110101111=>7 110110000=>9 110110001=>8 110110010=>9 110110011=>7 110110100=>9 110110101=>8 110110110=>3 110110111=>7 110111000=>9 110111001=>8 110111010=>9 110111011=>4 110111100=>9 110111101=>5 110111110=>6 110111111=>7 111000000=>9 111000001=>8 111000010=>9 111000011=>7 111000100=>9 111000101=>8 111000110=>9 111000111=>6 111001000=>9 111001001=>8 111001010=>9 111001011=>7 111001100=>9 111001101=>8 111001110=>5 111001111=>6 111010000=>9 111010001=>8 111010010=>9 111010011=>7 111010100=>9 111010101=>8 111010110=>9 111010111=>6 111011000=>9 111011001=>8 111011010=>9 111011011=>7 111011100=>9 111011101=>4 111011110=>5 111011111=>6 111100000=>9 111100001=>8 111100010=>9 111100011=>7 111100100=>9 111100101=>8 111100110=>9 111100111=>6 111101000=>9 111101001=>8 111101010=>9 111101011=>7 111101100=>9 111101101=>8 111101110=>9 111101111=>5 111110000=>9 111110001=>8 111110010=>9 111110011=>7 111110100=>9 111110101=>8 111110110=>9 111110111=>6 111111000=>9 111111001=>8 111111010=>9 111111011=>7 111111100=>9 111111101=>8 111111110=>9 111111111=>1 0000000001=>10 0010000001=>7 0010101101=>10 0010101011=>10 0010100111=>10 0010011101=>10 0010011011=>10 0010010111=>10 0010001111=>10 0001110101=>10 0001110011=>10 0001101101=>10 0001101011=>10 0001100111=>10 0001011101=>10 0001011011=>10 0001010111=>10 0001001111=>10 0000111101=>10 0000111011=>10 0000110111=>10 0000101111=>10 0000011111=>10 0000000000=>1 0000000110=>9 0000011000=>7 0000011110=>9 0000010010=>9 0001100000=>7 0001100110=>9 0001111000=>7 0001111110=>9 0001110010=>9 0001001000=>7 0001001110=>9 0001000010=>5 0001011010=>9 0010101010=>9 0010101000=>8 0010101100=>8 0010100100=>8 0010010100=>8 0001010100=>8 0010101110=>9 0010100000=>8 0010000100=>5 0000010100=>8 0000000010=>9 0000001110=>9 0000111110=>9 0000000100=>8 0000001010=>9 0000010110=>9 0000101110=>9 0001011110=>9 0001101110=>9 0001110110=>9 0001111010=>9 0001111100=>8 0000000101=>10 0000001101=>10 0000011101=>10 0001111101=>10 0000001001=>10 0000010101=>10 0000101101=>10 0010110001=>7 0001100001=>6 0001000001=>6 0000111111=>10 0001110100=>8 0001101100=>8 0010011100=>8 0001011100=>8 0000111100=>8 0001101010=>9 0010011010=>9 0000111010=>9 0010100110=>9 0010010110=>9 0001010110=>9 0000110110=>9 0010001110=>9 0001101001=>10 0000110001=>10 0000010001=>10 0000001100=>8 0000011001=>10 0000110011=>10 0000110100=>8 0000000011=>10 0000011011=>10 0001101111=>10 0000110101=>10 0010000010=>6 0001000011=>10 0010011110=>9 0001010000=>7 0001000100=>4 0001010101=>10 0001001011=>10 0001100011=>5 0001110111=>10 0010000000=>8 0000000111=>10 0000001111=>10 0001111111=>10 0000001011=>10 0000010111=>10 0001011111=>10 0001111001=>10 0000011010=>9 0000101010=>9 0000100101=>10 0010010001=>7 0010000101=>10 0010010101=>10 0010010011=>10 0000101011=>10 0001000111=>10 0000100111=>10 0010010010=>3 0001001010=>9 0001001001=>10 0001000101=>10 0000100011=>10 0000100100=>8 0000100010=>9 0010110000=>8 0000011100=>8 0000001000=>7 0000101100=>8 0010101111=>10 0000101000=>7 0010001000=>4 0001001100=>8 0001000110=>9 0001100100=>8 0001100010=>9 0000100110=>9 0000110010=>9 0010010000=>8 0001010010=>9 0001000000=>7 0001011001=>10 0001100101=>10 0001110001=>6 0010011001=>7 0010100101=>5 0010101001=>7 0010011111=>10 0000111001=>10 0010001101=>10 0001001101=>10 0001010001=>6 0001010011=>10 0001111011=>10 0010011000=>8 0001011000=>7 0000100000=>6 0010001011=>10 0010000111=>10 0000010011=>10 0010001100=>8 0010000110=>9 0000110000=>6 0000100001=>5 0010100011=>10 0010100001=>7 0000111000=>7 0001101000=>7 0000010000=>6 0000101001=>10 0010100010=>6 0010001001=>7 0010000011=>10 0010001010=>9 0001110000=>7
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Description
The minimal period of a binary word.
This is the smallest natural number $p$ such that $w_i=w_{i+p}$ for all $i\in\{1,\dots,|w|-p\}$.
Code
def statistic(w):
    return w.minimal_period()

Created
Oct 16, 2016 at 22:07 by Martin Rubey
Updated
Oct 16, 2016 at 22:07 by Martin Rubey