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

Created
Feb 12, 2016 at 22:05 by Martin Rubey
Updated
Feb 12, 2016 at 22:05 by Martin Rubey