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

Created
Jun 11, 2019 at 07:24 by Martin Rubey
Updated
Mar 05, 2020 at 13:41 by Martin Rubey