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

Created
Dec 21, 2022 at 10:52 by Martin Rubey
Updated
Dec 21, 2022 at 10:52 by Martin Rubey