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

Created
Jun 11, 2019 at 11:28 by Martin Rubey
Updated
Jun 11, 2019 at 11:28 by Martin Rubey