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Identifier
Values
=>
0=>1 1=>1 00=>2 01=>1 10=>1 11=>2 000=>3 001=>2 010=>3 011=>1 100=>1 101=>3 110=>2 111=>3 0000=>4 0001=>3 0010=>2 0011=>2 0100=>3 0101=>3 0110=>4 0111=>1 1000=>1 1001=>4 1010=>3 1011=>3 1100=>2 1101=>2 1110=>3 1111=>4 00000=>5 00001=>4 00010=>3 00011=>3 00100=>5 00101=>2 00110=>2 00111=>2 01000=>3 01001=>3 01010=>5 01011=>3 01100=>4 01101=>4 01110=>5 01111=>1 10000=>1 10001=>5 10010=>4 10011=>4 10100=>3 10101=>5 10110=>3 10111=>3 11000=>2 11001=>2 11010=>2 11011=>5 11100=>3 11101=>3 11110=>4 11111=>5 000000=>6 000001=>5 000010=>4 000011=>4 000100=>3 000101=>3 000110=>3 000111=>3 001000=>5 001001=>5 001010=>2 001011=>2 001100=>6 001101=>2 001110=>2 001111=>2 010000=>3 010001=>3 010010=>6 010011=>3 010100=>5 010101=>5 010110=>3 010111=>3 011000=>4 011001=>4 011010=>4 011011=>4 011100=>5 011101=>5 011110=>6 011111=>1 100000=>1 100001=>6 100010=>5 100011=>5 100100=>4 100101=>4 100110=>4 100111=>4 101000=>3 101001=>3 101010=>5 101011=>5 101100=>3 101101=>6 101110=>3 101111=>3 110000=>2 110001=>2 110010=>2 110011=>6 110100=>2 110101=>2 110110=>5 110111=>5 111000=>3 111001=>3 111010=>3 111011=>3 111100=>4 111101=>4 111110=>5 111111=>6 0000000=>7 0000001=>6 0000010=>5 0000011=>5 0000100=>4 0000101=>4 0000110=>4 0000111=>4 0001000=>7 0001001=>3 0001010=>3 0001011=>3 0001100=>3 0001101=>3 0001110=>3 0001111=>3 0010000=>5 0010001=>5 0010010=>5 0010011=>5 0010100=>7 0010101=>2 0010110=>2 0010111=>2 0011000=>6 0011001=>6 0011010=>2 0011011=>2 0011100=>7 0011101=>2 0011110=>2 0011111=>2 0100000=>3 0100001=>3 0100010=>7 0100011=>3 0100100=>6 0100101=>6 0100110=>3 0100111=>3 0101000=>5 0101001=>5 0101010=>7 0101011=>5 0101100=>3 0101101=>3 0101110=>3 0101111=>3 0110000=>4 0110001=>4 0110010=>4 0110011=>4 0110100=>4 0110101=>4 0110110=>7 0110111=>4 0111000=>5 0111001=>5 0111010=>5 0111011=>5 0111100=>6 0111101=>6 0111110=>7 0111111=>1 1000000=>1 1000001=>7 1000010=>6 1000011=>6 1000100=>5 1000101=>5 1000110=>5 1000111=>5 1001000=>4 1001001=>7 1001010=>4 1001011=>4 1001100=>4 1001101=>4 1001110=>4 1001111=>4 1010000=>3 1010001=>3 1010010=>3 1010011=>3 1010100=>5 1010101=>7 1010110=>5 1010111=>5 1011000=>3 1011001=>3 1011010=>6 1011011=>6 1011100=>3 1011101=>7 1011110=>3 1011111=>3 1100000=>2 1100001=>2 1100010=>2 1100011=>7 1100100=>2 1100101=>2 1100110=>6 1100111=>6 1101000=>2 1101001=>2 1101010=>2 1101011=>7 1101100=>5 1101101=>5 1101110=>5 1101111=>5 1110000=>3 1110001=>3 1110010=>3 1110011=>3 1110100=>3 1110101=>3 1110110=>3 1110111=>7 1111000=>4 1111001=>4 1111010=>4 1111011=>4 1111100=>5 1111101=>5 1111110=>6 1111111=>7 00000000=>8 00000001=>7 00000010=>6 00000011=>6 00000100=>5 00000101=>5 00000110=>5 00000111=>5 00001000=>4 00001001=>4 00001010=>4 00001011=>4 00001100=>4 00001101=>4 00001110=>4 00001111=>4 00010000=>7 00010001=>7 00010010=>3 00010011=>3 00010100=>3 00010101=>3 00010110=>3 00010111=>3 00011000=>8 00011001=>3 00011010=>3 00011011=>3 00011100=>3 00011101=>3 00011110=>3 00011111=>3 00100000=>5 00100001=>5 00100010=>5 00100011=>5 00100100=>8 00100101=>5 00100110=>5 00100111=>5 00101000=>7 00101001=>7 00101010=>2 00101011=>2 00101100=>2 00101101=>2 00101110=>2 00101111=>2 00110000=>6 00110001=>6 00110010=>6 00110011=>6 00110100=>2 00110101=>2 00110110=>2 00110111=>2 00111000=>7 00111001=>7 00111010=>2 00111011=>2 00111100=>8 00111101=>2 00111110=>2 00111111=>2 01000000=>3 01000001=>3 01000010=>8 01000011=>3 01000100=>7 01000101=>7 01000110=>3 01000111=>3 01001000=>6 01001001=>6 01001010=>6 01001011=>6 01001100=>3 01001101=>3 01001110=>3 01001111=>3 01010000=>5 01010001=>5 01010010=>5 01010011=>5 01010100=>7 01010101=>7 01010110=>5 01010111=>5 01011000=>3 01011001=>3 01011010=>8 01011011=>3 01011100=>3 01011101=>3 01011110=>3 01011111=>3 01100000=>4 01100001=>4 01100010=>4 01100011=>4 01100100=>4 01100101=>4 01100110=>8 01100111=>4 01101000=>4 01101001=>4 01101010=>4 01101011=>4 01101100=>7 01101101=>7 01101110=>4 01101111=>4 01110000=>5 01110001=>5 01110010=>5 01110011=>5 01110100=>5 01110101=>5 01110110=>5 01110111=>5 01111000=>6 01111001=>6 01111010=>6 01111011=>6 01111100=>7 01111101=>7 01111110=>8 01111111=>1 10000000=>1 10000001=>8 10000010=>7 10000011=>7 10000100=>6 10000101=>6 10000110=>6 10000111=>6 10001000=>5 10001001=>5 10001010=>5 10001011=>5 10001100=>5 10001101=>5 10001110=>5 10001111=>5 10010000=>4 10010001=>4 10010010=>7 10010011=>7 10010100=>4 10010101=>4 10010110=>4 10010111=>4 10011000=>4 10011001=>8 10011010=>4 10011011=>4 10011100=>4 10011101=>4 10011110=>4 10011111=>4 10100000=>3 10100001=>3 10100010=>3 10100011=>3 10100100=>3 10100101=>8 10100110=>3 10100111=>3 10101000=>5 10101001=>5 10101010=>7 10101011=>7 10101100=>5 10101101=>5 10101110=>5 10101111=>5 10110000=>3 10110001=>3 10110010=>3 10110011=>3 10110100=>6 10110101=>6 10110110=>6 10110111=>6 10111000=>3 10111001=>3 10111010=>7 10111011=>7 10111100=>3 10111101=>8 10111110=>3 10111111=>3 11000000=>2 11000001=>2 11000010=>2 11000011=>8 11000100=>2 11000101=>2 11000110=>7 11000111=>7 11001000=>2 11001001=>2 11001010=>2 11001011=>2 11001100=>6 11001101=>6 11001110=>6 11001111=>6 11010000=>2 11010001=>2 11010010=>2 11010011=>2 11010100=>2 11010101=>2 11010110=>7 11010111=>7 11011000=>5 11011001=>5 11011010=>5 11011011=>8 11011100=>5 11011101=>5 11011110=>5 11011111=>5 11100000=>3 11100001=>3 11100010=>3 11100011=>3 11100100=>3 11100101=>3 11100110=>3 11100111=>8 11101000=>3 11101001=>3 11101010=>3 11101011=>3 11101100=>3 11101101=>3 11101110=>7 11101111=>7 11110000=>4 11110001=>4 11110010=>4 11110011=>4 11110100=>4 11110101=>4 11110110=>4 11110111=>4 11111000=>5 11111001=>5 11111010=>5 11111011=>5 11111100=>6 11111101=>6 11111110=>7 11111111=>8 000000000=>9 000000001=>8 000000010=>7 000000011=>7 000000100=>6 000000101=>6 000000110=>6 000000111=>6 000001000=>5 000001001=>5 000001010=>5 000001011=>5 000001100=>5 000001101=>5 000001110=>5 000001111=>5 000010000=>9 000010001=>4 000010010=>4 000010011=>4 000010100=>4 000010101=>4 000010110=>4 000010111=>4 000011000=>4 000011001=>4 000011010=>4 000011011=>4 000011100=>4 000011101=>4 000011110=>4 000011111=>4 000100000=>7 000100001=>7 000100010=>7 000100011=>7 000100100=>3 000100101=>3 000100110=>3 000100111=>3 000101000=>9 000101001=>3 000101010=>3 000101011=>3 000101100=>3 000101101=>3 000101110=>3 000101111=>3 000110000=>8 000110001=>8 000110010=>3 000110011=>3 000110100=>3 000110101=>3 000110110=>3 000110111=>3 000111000=>9 000111001=>3 000111010=>3 000111011=>3 000111100=>3 000111101=>3 000111110=>3 000111111=>3 001000000=>5 001000001=>5 001000010=>5 001000011=>5 001000100=>9 001000101=>5 001000110=>5 001000111=>5 001001000=>8 001001001=>8 001001010=>5 001001011=>5 001001100=>5 001001101=>5 001001110=>5 001001111=>5 001010000=>7 001010001=>7 001010010=>7 001010011=>7 001010100=>9 001010101=>2 001010110=>2 001010111=>2 001011000=>2 001011001=>2 001011010=>2 001011011=>2 001011100=>2 001011101=>2 001011110=>2 001011111=>2 001100000=>6 001100001=>6 001100010=>6 001100011=>6 001100100=>6 001100101=>6 001100110=>6 001100111=>6 001101000=>2 001101001=>2 001101010=>2 001101011=>2 001101100=>9 001101101=>2 001101110=>2 001101111=>2 001110000=>7 001110001=>7 001110010=>7 001110011=>7 001110100=>2 001110101=>2 001110110=>2 001110111=>2 001111000=>8 001111001=>8 001111010=>2 001111011=>2 001111100=>9 001111101=>2 001111110=>2 001111111=>2 010000000=>3 010000001=>3 010000010=>9 010000011=>3 010000100=>8 010000101=>8 010000110=>3 010000111=>3 010001000=>7 010001001=>7 010001010=>7 010001011=>7 010001100=>3 010001101=>3 010001110=>3 010001111=>3 010010000=>6 010010001=>6 010010010=>9 010010011=>6 010010100=>6 010010101=>6 010010110=>6 010010111=>6 010011000=>3 010011001=>3 010011010=>3 010011011=>3 010011100=>3 010011101=>3 010011110=>3 010011111=>3 010100000=>5 010100001=>5 010100010=>5 010100011=>5 010100100=>5 010100101=>5 010100110=>5 010100111=>5 010101000=>7 010101001=>7 010101010=>9 010101011=>7 010101100=>5 010101101=>5 010101110=>5 010101111=>5 010110000=>3 010110001=>3 010110010=>3 010110011=>3 010110100=>8 010110101=>8 010110110=>3 010110111=>3 010111000=>3 010111001=>3 010111010=>9 010111011=>3 010111100=>3 010111101=>3 010111110=>3 010111111=>3 011000000=>4 011000001=>4 011000010=>4 011000011=>4 011000100=>4 011000101=>4 011000110=>9 011000111=>4 011001000=>4 011001001=>4 011001010=>4 011001011=>4 011001100=>8 011001101=>8 011001110=>4 011001111=>4 011010000=>4 011010001=>4 011010010=>4 011010011=>4 011010100=>4 011010101=>4 011010110=>9 011010111=>4 011011000=>7 011011001=>7 011011010=>7 011011011=>7 011011100=>4 011011101=>4 011011110=>4 011011111=>4 011100000=>5 011100001=>5 011100010=>5 011100011=>5 011100100=>5 011100101=>5 011100110=>5 011100111=>5 011101000=>5 011101001=>5 011101010=>5 011101011=>5 011101100=>5 011101101=>5 011101110=>9 011101111=>5 011110000=>6 011110001=>6 011110010=>6 011110011=>6 011110100=>6 011110101=>6 011110110=>6 011110111=>6 011111000=>7 011111001=>7 011111010=>7 011111011=>7 011111100=>8 011111101=>8 011111110=>9 011111111=>1 100000000=>1 100000001=>9 100000010=>8 100000011=>8 100000100=>7 100000101=>7 100000110=>7 100000111=>7 100001000=>6 100001001=>6 100001010=>6 100001011=>6 100001100=>6 100001101=>6 100001110=>6 100001111=>6 100010000=>5 100010001=>9 100010010=>5 100010011=>5 100010100=>5 100010101=>5 100010110=>5 100010111=>5 100011000=>5 100011001=>5 100011010=>5 100011011=>5 100011100=>5 100011101=>5 100011110=>5 100011111=>5 100100000=>4 100100001=>4 100100010=>4 100100011=>4 100100100=>7 100100101=>7 100100110=>7 100100111=>7 100101000=>4 100101001=>9 100101010=>4 100101011=>4 100101100=>4 100101101=>4 100101110=>4 100101111=>4 100110000=>4 100110001=>4 100110010=>8 100110011=>8 100110100=>4 100110101=>4 100110110=>4 100110111=>4 100111000=>4 100111001=>9 100111010=>4 100111011=>4 100111100=>4 100111101=>4 100111110=>4 100111111=>4 101000000=>3 101000001=>3 101000010=>3 101000011=>3 101000100=>3 101000101=>9 101000110=>3 101000111=>3 101001000=>3 101001001=>3 101001010=>8 101001011=>8 101001100=>3 101001101=>3 101001110=>3 101001111=>3 101010000=>5 101010001=>5 101010010=>5 101010011=>5 101010100=>7 101010101=>9 101010110=>7 101010111=>7 101011000=>5 101011001=>5 101011010=>5 101011011=>5 101011100=>5 101011101=>5 101011110=>5 101011111=>5 101100000=>3 101100001=>3 101100010=>3 101100011=>3 101100100=>3 101100101=>3 101100110=>3 101100111=>3 101101000=>6 101101001=>6 101101010=>6 101101011=>6 101101100=>6 101101101=>9 101101110=>6 101101111=>6 101110000=>3 101110001=>3 101110010=>3 101110011=>3 101110100=>7 101110101=>7 101110110=>7 101110111=>7 101111000=>3 101111001=>3 101111010=>8 101111011=>8 101111100=>3 101111101=>9 101111110=>3 101111111=>3 110000000=>2 110000001=>2 110000010=>2 110000011=>9 110000100=>2 110000101=>2 110000110=>8 110000111=>8 110001000=>2 110001001=>2 110001010=>2 110001011=>2 110001100=>7 110001101=>7 110001110=>7 110001111=>7 110010000=>2 110010001=>2 110010010=>2 110010011=>9 110010100=>2 110010101=>2 110010110=>2 110010111=>2 110011000=>6 110011001=>6 110011010=>6 110011011=>6 110011100=>6 110011101=>6 110011110=>6 110011111=>6 110100000=>2 110100001=>2 110100010=>2 110100011=>2 110100100=>2 110100101=>2 110100110=>2 110100111=>2 110101000=>2 110101001=>2 110101010=>2 110101011=>9 110101100=>7 110101101=>7 110101110=>7 110101111=>7 110110000=>5 110110001=>5 110110010=>5 110110011=>5 110110100=>5 110110101=>5 110110110=>8 110110111=>8 110111000=>5 110111001=>5 110111010=>5 110111011=>9 110111100=>5 110111101=>5 110111110=>5 110111111=>5 111000000=>3 111000001=>3 111000010=>3 111000011=>3 111000100=>3 111000101=>3 111000110=>3 111000111=>9 111001000=>3 111001001=>3 111001010=>3 111001011=>3 111001100=>3 111001101=>3 111001110=>8 111001111=>8 111010000=>3 111010001=>3 111010010=>3 111010011=>3 111010100=>3 111010101=>3 111010110=>3 111010111=>9 111011000=>3 111011001=>3 111011010=>3 111011011=>3 111011100=>7 111011101=>7 111011110=>7 111011111=>7 111100000=>4 111100001=>4 111100010=>4 111100011=>4 111100100=>4 111100101=>4 111100110=>4 111100111=>4 111101000=>4 111101001=>4 111101010=>4 111101011=>4 111101100=>4 111101101=>4 111101110=>4 111101111=>9 111110000=>5 111110001=>5 111110010=>5 111110011=>5 111110100=>5 111110101=>5 111110110=>5 111110111=>5 111111000=>6 111111001=>6 111111010=>6 111111011=>6 111111100=>7 111111101=>7 111111110=>8 111111111=>9
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Description
The length of the longest palindromic prefix of a binary word.
References
[1] Gabric, D., Shallit, J. Borders, Palindrome Prefixes, and Square Prefixes arXiv:1906.03689
Code
def statistic(w):
    return max(k for k in range(len(w)+1) if w[:k] == w[:k][::-1])

Created
Jun 11, 2019 at 07:18 by Martin Rubey
Updated
Mar 05, 2020 at 14:09 by Martin Rubey