edit this statistic or download as text // json
Identifier
Values
=>
0=>0 1=>0 00=>0 01=>0 10=>1 11=>0 000=>0 001=>0 010=>2 011=>0 100=>1 101=>1 110=>2 111=>0 0000=>0 0001=>0 0010=>3 0011=>0 0100=>2 0101=>2 0110=>3 0111=>0 1000=>1 1001=>1 1010=>4 1011=>1 1100=>2 1101=>2 1110=>3 1111=>0 00000=>0 00001=>0 00010=>4 00011=>0 00100=>3 00101=>3 00110=>4 00111=>0 01000=>2 01001=>2 01010=>6 01011=>2 01100=>3 01101=>3 01110=>4 01111=>0 10000=>1 10001=>1 10010=>5 10011=>1 10100=>4 10101=>4 10110=>5 10111=>1 11000=>2 11001=>2 11010=>6 11011=>2 11100=>3 11101=>3 11110=>4 11111=>0 000000=>0 000001=>0 000010=>5 000011=>0 000100=>4 000101=>4 000110=>5 000111=>0 001000=>3 001001=>3 001010=>8 001011=>3 001100=>4 001101=>4 001110=>5 001111=>0 010000=>2 010001=>2 010010=>7 010011=>2 010100=>6 010101=>6 010110=>7 010111=>2 011000=>3 011001=>3 011010=>8 011011=>3 011100=>4 011101=>4 011110=>5 011111=>0 100000=>1 100001=>1 100010=>6 100011=>1 100100=>5 100101=>5 100110=>6 100111=>1 101000=>4 101001=>4 101010=>9 101011=>4 101100=>5 101101=>5 101110=>6 101111=>1 110000=>2 110001=>2 110010=>7 110011=>2 110100=>6 110101=>6 110110=>7 110111=>2 111000=>3 111001=>3 111010=>8 111011=>3 111100=>4 111101=>4 111110=>5 111111=>0 0000000=>0 0000001=>0 0000010=>6 0000011=>0 0000100=>5 0000101=>5 0000110=>6 0000111=>0 0001000=>4 0001001=>4 0001010=>10 0001011=>4 0001100=>5 0001101=>5 0001110=>6 0001111=>0 0010000=>3 0010001=>3 0010010=>9 0010011=>3 0010100=>8 0010101=>8 0010110=>9 0010111=>3 0011000=>4 0011001=>4 0011010=>10 0011011=>4 0011100=>5 0011101=>5 0011110=>6 0011111=>0 0100000=>2 0100001=>2 0100010=>8 0100011=>2 0100100=>7 0100101=>7 0100110=>8 0100111=>2 0101000=>6 0101001=>6 0101010=>12 0101011=>6 0101100=>7 0101101=>7 0101110=>8 0101111=>2 0110000=>3 0110001=>3 0110010=>9 0110011=>3 0110100=>8 0110101=>8 0110110=>9 0110111=>3 0111000=>4 0111001=>4 0111010=>10 0111011=>4 0111100=>5 0111101=>5 0111110=>6 0111111=>0 1000000=>1 1000001=>1 1000010=>7 1000011=>1 1000100=>6 1000101=>6 1000110=>7 1000111=>1 1001000=>5 1001001=>5 1001010=>11 1001011=>5 1001100=>6 1001101=>6 1001110=>7 1001111=>1 1010000=>4 1010001=>4 1010010=>10 1010011=>4 1010100=>9 1010101=>9 1010110=>10 1010111=>4 1011000=>5 1011001=>5 1011010=>11 1011011=>5 1011100=>6 1011101=>6 1011110=>7 1011111=>1 1100000=>2 1100001=>2 1100010=>8 1100011=>2 1100100=>7 1100101=>7 1100110=>8 1100111=>2 1101000=>6 1101001=>6 1101010=>12 1101011=>6 1101100=>7 1101101=>7 1101110=>8 1101111=>2 1110000=>3 1110001=>3 1110010=>9 1110011=>3 1110100=>8 1110101=>8 1110110=>9 1110111=>3 1111000=>4 1111001=>4 1111010=>10 1111011=>4 1111100=>5 1111101=>5 1111110=>6 1111111=>0 00000000=>0 00000001=>0 00000010=>7 00000011=>0 00000100=>6 00000101=>6 00000110=>7 00000111=>0 00001000=>5 00001001=>5 00001010=>12 00001011=>5 00001100=>6 00001101=>6 00001110=>7 00001111=>0 00010000=>4 00010001=>4 00010010=>11 00010011=>4 00010100=>10 00010101=>10 00010110=>11 00010111=>4 00011000=>5 00011001=>5 00011010=>12 00011011=>5 00011100=>6 00011101=>6 00011110=>7 00011111=>0 00100000=>3 00100001=>3 00100010=>10 00100011=>3 00100100=>9 00100101=>9 00100110=>10 00100111=>3 00101000=>8 00101001=>8 00101010=>15 00101011=>8 00101100=>9 00101101=>9 00101110=>10 00101111=>3 00110000=>4 00110001=>4 00110010=>11 00110011=>4 00110100=>10 00110101=>10 00110110=>11 00110111=>4 00111000=>5 00111001=>5 00111010=>12 00111011=>5 00111100=>6 00111101=>6 00111110=>7 00111111=>0 01000000=>2 01000001=>2 01000010=>9 01000011=>2 01000100=>8 01000101=>8 01000110=>9 01000111=>2 01001000=>7 01001001=>7 01001010=>14 01001011=>7 01001100=>8 01001101=>8 01001110=>9 01001111=>2 01010000=>6 01010001=>6 01010010=>13 01010011=>6 01010100=>12 01010101=>12 01010110=>13 01010111=>6 01011000=>7 01011001=>7 01011010=>14 01011011=>7 01011100=>8 01011101=>8 01011110=>9 01011111=>2 01100000=>3 01100001=>3 01100010=>10 01100011=>3 01100100=>9 01100101=>9 01100110=>10 01100111=>3 01101000=>8 01101001=>8 01101010=>15 01101011=>8 01101100=>9 01101101=>9 01101110=>10 01101111=>3 01110000=>4 01110001=>4 01110010=>11 01110011=>4 01110100=>10 01110101=>10 01110110=>11 01110111=>4 01111000=>5 01111001=>5 01111010=>12 01111011=>5 01111100=>6 01111101=>6 01111110=>7 01111111=>0 10000000=>1 10000001=>1 10000010=>8 10000011=>1 10000100=>7 10000101=>7 10000110=>8 10000111=>1 10001000=>6 10001001=>6 10001010=>13 10001011=>6 10001100=>7 10001101=>7 10001110=>8 10001111=>1 10010000=>5 10010001=>5 10010010=>12 10010011=>5 10010100=>11 10010101=>11 10010110=>12 10010111=>5 10011000=>6 10011001=>6 10011010=>13 10011011=>6 10011100=>7 10011101=>7 10011110=>8 10011111=>1 10100000=>4 10100001=>4 10100010=>11 10100011=>4 10100100=>10 10100101=>10 10100110=>11 10100111=>4 10101000=>9 10101001=>9 10101010=>16 10101011=>9 10101100=>10 10101101=>10 10101110=>11 10101111=>4 10110000=>5 10110001=>5 10110010=>12 10110011=>5 10110100=>11 10110101=>11 10110110=>12 10110111=>5 10111000=>6 10111001=>6 10111010=>13 10111011=>6 10111100=>7 10111101=>7 10111110=>8 10111111=>1 11000000=>2 11000001=>2 11000010=>9 11000011=>2 11000100=>8 11000101=>8 11000110=>9 11000111=>2 11001000=>7 11001001=>7 11001010=>14 11001011=>7 11001100=>8 11001101=>8 11001110=>9 11001111=>2 11010000=>6 11010001=>6 11010010=>13 11010011=>6 11010100=>12 11010101=>12 11010110=>13 11010111=>6 11011000=>7 11011001=>7 11011010=>14 11011011=>7 11011100=>8 11011101=>8 11011110=>9 11011111=>2 11100000=>3 11100001=>3 11100010=>10 11100011=>3 11100100=>9 11100101=>9 11100110=>10 11100111=>3 11101000=>8 11101001=>8 11101010=>15 11101011=>8 11101100=>9 11101101=>9 11101110=>10 11101111=>3 11110000=>4 11110001=>4 11110010=>11 11110011=>4 11110100=>10 11110101=>10 11110110=>11 11110111=>4 11111000=>5 11111001=>5 11111010=>12 11111011=>5 11111100=>6 11111101=>6 11111110=>7 11111111=>0 000000000=>0 000000001=>0 000000010=>8 000000011=>0 000000100=>7 000000101=>7 000000110=>8 000000111=>0 000001000=>6 000001001=>6 000001010=>14 000001011=>6 000001100=>7 000001101=>7 000001110=>8 000001111=>0 000010000=>5 000010001=>5 000010010=>13 000010011=>5 000010100=>12 000010101=>12 000010110=>13 000010111=>5 000011000=>6 000011001=>6 000011010=>14 000011011=>6 000011100=>7 000011101=>7 000011110=>8 000011111=>0 000100000=>4 000100001=>4 000100010=>12 000100011=>4 000100100=>11 000100101=>11 000100110=>12 000100111=>4 000101000=>10 000101001=>10 000101010=>18 000101011=>10 000101100=>11 000101101=>11 000101110=>12 000101111=>4 000110000=>5 000110001=>5 000110010=>13 000110011=>5 000110100=>12 000110101=>12 000110110=>13 000110111=>5 000111000=>6 000111001=>6 000111010=>14 000111011=>6 000111100=>7 000111101=>7 000111110=>8 000111111=>0 001000000=>3 001000001=>3 001000010=>11 001000011=>3 001000100=>10 001000101=>10 001000110=>11 001000111=>3 001001000=>9 001001001=>9 001001010=>17 001001011=>9 001001100=>10 001001101=>10 001001110=>11 001001111=>3 001010000=>8 001010001=>8 001010010=>16 001010011=>8 001010100=>15 001010101=>15 001010110=>16 001010111=>8 001011000=>9 001011001=>9 001011010=>17 001011011=>9 001011100=>10 001011101=>10 001011110=>11 001011111=>3 001100000=>4 001100001=>4 001100010=>12 001100011=>4 001100100=>11 001100101=>11 001100110=>12 001100111=>4 001101000=>10 001101001=>10 001101010=>18 001101011=>10 001101100=>11 001101101=>11 001101110=>12 001101111=>4 001110000=>5 001110001=>5 001110010=>13 001110011=>5 001110100=>12 001110101=>12 001110110=>13 001110111=>5 001111000=>6 001111001=>6 001111010=>14 001111011=>6 001111100=>7 001111101=>7 001111110=>8 001111111=>0 010000000=>2 010000001=>2 010000010=>10 010000011=>2 010000100=>9 010000101=>9 010000110=>10 010000111=>2 010001000=>8 010001001=>8 010001010=>16 010001011=>8 010001100=>9 010001101=>9 010001110=>10 010001111=>2 010010000=>7 010010001=>7 010010010=>15 010010011=>7 010010100=>14 010010101=>14 010010110=>15 010010111=>7 010011000=>8 010011001=>8 010011010=>16 010011011=>8 010011100=>9 010011101=>9 010011110=>10 010011111=>2 010100000=>6 010100001=>6 010100010=>14 010100011=>6 010100100=>13 010100101=>13 010100110=>14 010100111=>6 010101000=>12 010101001=>12 010101010=>20 010101011=>12 010101100=>13 010101101=>13 010101110=>14 010101111=>6 010110000=>7 010110001=>7 010110010=>15 010110011=>7 010110100=>14 010110101=>14 010110110=>15 010110111=>7 010111000=>8 010111001=>8 010111010=>16 010111011=>8 010111100=>9 010111101=>9 010111110=>10 010111111=>2 011000000=>3 011000001=>3 011000010=>11 011000011=>3 011000100=>10 011000101=>10 011000110=>11 011000111=>3 011001000=>9 011001001=>9 011001010=>17 011001011=>9 011001100=>10 011001101=>10 011001110=>11 011001111=>3 011010000=>8 011010001=>8 011010010=>16 011010011=>8 011010100=>15 011010101=>15 011010110=>16 011010111=>8 011011000=>9 011011001=>9 011011010=>17 011011011=>9 011011100=>10 011011101=>10 011011110=>11 011011111=>3 011100000=>4 011100001=>4 011100010=>12 011100011=>4 011100100=>11 011100101=>11 011100110=>12 011100111=>4 011101000=>10 011101001=>10 011101010=>18 011101011=>10 011101100=>11 011101101=>11 011101110=>12 011101111=>4 011110000=>5 011110001=>5 011110010=>13 011110011=>5 011110100=>12 011110101=>12 011110110=>13 011110111=>5 011111000=>6 011111001=>6 011111010=>14 011111011=>6 011111100=>7 011111101=>7 011111110=>8 011111111=>0 100000000=>1 100000001=>1 100000010=>9 100000011=>1 100000100=>8 100000101=>8 100000110=>9 100000111=>1 100001000=>7 100001001=>7 100001010=>15 100001011=>7 100001100=>8 100001101=>8 100001110=>9 100001111=>1 100010000=>6 100010001=>6 100010010=>14 100010011=>6 100010100=>13 100010101=>13 100010110=>14 100010111=>6 100011000=>7 100011001=>7 100011010=>15 100011011=>7 100011100=>8 100011101=>8 100011110=>9 100011111=>1 100100000=>5 100100001=>5 100100010=>13 100100011=>5 100100100=>12 100100101=>12 100100110=>13 100100111=>5 100101000=>11 100101001=>11 100101010=>19 100101011=>11 100101100=>12 100101101=>12 100101110=>13 100101111=>5 100110000=>6 100110001=>6 100110010=>14 100110011=>6 100110100=>13 100110101=>13 100110110=>14 100110111=>6 100111000=>7 100111001=>7 100111010=>15 100111011=>7 100111100=>8 100111101=>8 100111110=>9 100111111=>1 101000000=>4 101000001=>4 101000010=>12 101000011=>4 101000100=>11 101000101=>11 101000110=>12 101000111=>4 101001000=>10 101001001=>10 101001010=>18 101001011=>10 101001100=>11 101001101=>11 101001110=>12 101001111=>4 101010000=>9 101010001=>9 101010010=>17 101010011=>9 101010100=>16 101010101=>16 101010110=>17 101010111=>9 101011000=>10 101011001=>10 101011010=>18 101011011=>10 101011100=>11 101011101=>11 101011110=>12 101011111=>4 101100000=>5 101100001=>5 101100010=>13 101100011=>5 101100100=>12 101100101=>12 101100110=>13 101100111=>5 101101000=>11 101101001=>11 101101010=>19 101101011=>11 101101100=>12 101101101=>12 101101110=>13 101101111=>5 101110000=>6 101110001=>6 101110010=>14 101110011=>6 101110100=>13 101110101=>13 101110110=>14 101110111=>6 101111000=>7 101111001=>7 101111010=>15 101111011=>7 101111100=>8 101111101=>8 101111110=>9 101111111=>1 110000000=>2 110000001=>2 110000010=>10 110000011=>2 110000100=>9 110000101=>9 110000110=>10 110000111=>2 110001000=>8 110001001=>8 110001010=>16 110001011=>8 110001100=>9 110001101=>9 110001110=>10 110001111=>2 110010000=>7 110010001=>7 110010010=>15 110010011=>7 110010100=>14 110010101=>14 110010110=>15 110010111=>7 110011000=>8 110011001=>8 110011010=>16 110011011=>8 110011100=>9 110011101=>9 110011110=>10 110011111=>2 110100000=>6 110100001=>6 110100010=>14 110100011=>6 110100100=>13 110100101=>13 110100110=>14 110100111=>6 110101000=>12 110101001=>12 110101010=>20 110101011=>12 110101100=>13 110101101=>13 110101110=>14 110101111=>6 110110000=>7 110110001=>7 110110010=>15 110110011=>7 110110100=>14 110110101=>14 110110110=>15 110110111=>7 110111000=>8 110111001=>8 110111010=>16 110111011=>8 110111100=>9 110111101=>9 110111110=>10 110111111=>2 111000000=>3 111000001=>3 111000010=>11 111000011=>3 111000100=>10 111000101=>10 111000110=>11 111000111=>3 111001000=>9 111001001=>9 111001010=>17 111001011=>9 111001100=>10 111001101=>10 111001110=>11 111001111=>3 111010000=>8 111010001=>8 111010010=>16 111010011=>8 111010100=>15 111010101=>15 111010110=>16 111010111=>8 111011000=>9 111011001=>9 111011010=>17 111011011=>9 111011100=>10 111011101=>10 111011110=>11 111011111=>3 111100000=>4 111100001=>4 111100010=>12 111100011=>4 111100100=>11 111100101=>11 111100110=>12 111100111=>4 111101000=>10 111101001=>10 111101010=>18 111101011=>10 111101100=>11 111101101=>11 111101110=>12 111101111=>4 111110000=>5 111110001=>5 111110010=>13 111110011=>5 111110100=>12 111110101=>12 111110110=>13 111110111=>5 111111000=>6 111111001=>6 111111010=>14 111111011=>6 111111100=>7 111111101=>7 111111110=>8 111111111=>0 1010101010=>25 1010101100=>17 1010110010=>19 1010110100=>18 1010111000=>11 1011001010=>21 1011001100=>13 1011010010=>20 1011010100=>19 1011011000=>12 1011100010=>15 1011100100=>14 1011101000=>13 1011110000=>7 1100101010=>23 1100101100=>15 1100110010=>17 1100110100=>16 1100111000=>9 1101001010=>22 1101001100=>14 1101010010=>21 1101010100=>20 1101011000=>13 1101100010=>16 1101100100=>15 1101101000=>14 1101110000=>8 1110001010=>19 1110001100=>11 1110010010=>18 1110010100=>17 1110011000=>10 1110100010=>17 1110100100=>16 1110101000=>15 1110110000=>9 1111000010=>13 1111000100=>12 1111001000=>11 1111010000=>10 1111100000=>5 1111111110=>9 1111111101=>8 1111000001=>4 1110111110=>12 1110100001=>8 1110011110=>12 1110010001=>9 1110001001=>10 1110000101=>11 1101111110=>11 1101100001=>7 1101010001=>12 1101001110=>15 1101001001=>13 1101000101=>14 1100110001=>8 1100101001=>14 1100100110=>16 1100100101=>15 1100011001=>9 1100010101=>16 1100010010=>17 1100001000=>9 1011111110=>10 1011111101=>9 1011100001=>6 1011010001=>11 1011001001=>12 1011000101=>13 1010111110=>13 1010110001=>10 1010101001=>16 1010100110=>18 1010100101=>17 1010011010=>20 1010011001=>11 1010010110=>19 1010010101=>18 1010001110=>13 1001111110=>10 1001111000=>8 1001110100=>15 1001110001=>7 1001101100=>14 1001101010=>22 1001101001=>13 1001100110=>15 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0010011111=>3 0000111001=>7 0010001101=>11 0001001101=>12 0001010001=>10 0001010011=>10 0001111011=>7 0010011000=>10 0001011000=>11 0000100000=>5 0010001011=>10 0010000111=>3 0000010011=>6 0010001100=>11 0010000110=>12 0000110000=>6 0000100001=>5 0010100011=>8 0010100001=>8 0000111000=>7 0001101000=>12 0000010000=>6 0000101001=>12 0010100010=>17 0010001001=>10 0010000011=>3 0010001010=>19 0001110000=>6 10000000000=>1 10000000010=>11 10000000110=>11 10000001110=>11 10000011110=>11 10000111110=>11 10001111110=>11 10011111110=>11 10111111110=>11 11111111110=>10 10000000100=>10 10000001010=>19 10000010110=>18 10000101110=>17 10001011110=>16 10010111110=>15 10101111110=>14 11011111110=>12 10000010000=>8 10000100010=>17 10001000010=>16 10000100100=>16 10001001010=>24 10001000100=>15 10000101000=>15 10010001010=>23 10001010010=>23 10010000100=>14 10001001000=>14 10010010010=>22 10001010100=>22 10010101010=>29 10010001000=>13 10100010010=>21 10010100010=>21 10010010100=>21 10100101010=>28 01111111111=>0 01111111101=>9 01111111001=>8 01111110001=>7 01111100001=>6 01111000001=>5 01110000001=>4 01100000001=>3 01000000001=>2 00000000001=>0 00000000010=>10 10101010101=>25 10101010010=>26 10101001001=>17 10101001010=>27 10101000100=>18 10100100101=>19 10100100010=>20 10100101001=>18 10100100100=>19 10100010001=>11 10100010100=>20 10100001000=>12 10010010101=>21 10010001001=>13 10010100101=>20 10010101001=>19 10010100100=>20 10010010001=>12 10001000101=>15 10001001001=>14 10001010001=>13 10000100001=>7 01001010101=>23 01001010010=>24 01001001001=>15 01001001010=>25 01001000100=>16 01000100101=>17 01000100010=>18 01000101001=>16 01000101010=>26 01000100100=>17 01000010001=>9 01000010010=>19 01000010100=>18 01000001000=>10 01010010101=>22 01010010010=>23 01010001001=>14 01010001010=>24 01010000100=>15 01010100101=>21 01010100010=>22 01010101001=>20 01010101010=>30 01010100100=>21 01010010001=>13 01010010100=>22 01010001000=>14 01001000101=>16 01001000010=>17 01001010001=>14 01001010100=>23 01001001000=>15 01000100001=>8 01000101000=>16 01000010000=>9 00100010101=>19 00100010010=>20 00100001001=>11 00100001010=>21 00100000100=>12 00100100101=>18 00100100010=>19 00100101001=>17 00100101010=>27 00100100100=>18 00100010001=>10 00100010100=>19 00100001000=>11 00101000101=>17 00101000010=>18 00101001001=>16 00101001010=>26 00101000100=>17 00101010001=>15 00101010010=>25 00101010100=>24 00101001000=>16 00100100001=>9 00100101000=>17 00100010000=>10 00010000101=>13 00010000010=>14 00010001001=>12 00010001010=>22 00010000100=>13 00010010001=>11 00010010010=>21 00010010100=>20 00010001000=>12 00010100001=>10 00010100010=>20 00010100100=>19 00010101000=>18 00010010000=>11 00001000001=>5 00001000010=>15 00001000100=>14 00001001000=>13 00001010000=>12 00000100000=>6 01000000000=>2 01000000011=>2 01000000111=>2 01000001111=>2 01000011111=>2 01000111111=>2 01001111111=>2 01011111111=>2 00000000101=>9 00000001101=>9 00000011101=>9 00000111101=>9 00001111101=>9 00011111101=>9 00111111101=>9 11111111101=>9 101010101010=>36 101010101100=>26 101010110010=>28 101010110100=>27 101010111000=>18 101011001010=>30 101011001100=>20 101011010010=>29 101011010100=>28 101011011000=>19 101011100010=>22 101011100100=>21 101011101000=>20 101011110000=>12 101100101010=>32 101100101100=>22 101100110010=>24 101100110100=>23 101100111000=>14 101101001010=>31 101101001100=>21 101101010010=>30 101101010100=>29 101101011000=>20 101101100010=>23 101101100100=>22 101101101000=>21 101101110000=>13 101110001010=>26 101110001100=>16 101110010010=>25 101110010100=>24 101110011000=>15 101110100010=>24 101110100100=>23 101110101000=>22 101110110000=>14 101111000010=>18 101111000100=>17 101111001000=>16 101111010000=>15 101111100000=>8 110010101010=>34 110010101100=>24 110010110010=>26 110010110100=>25 110010111000=>16 110011001010=>28 110011001100=>18 110011010010=>27 110011010100=>26 110011011000=>17 110011100010=>20 110011100100=>19 110011101000=>18 110011110000=>10 110100101010=>33 110100101100=>23 110100110010=>25 110100110100=>24 110100111000=>15 110101001010=>32 110101001100=>22 110101010010=>31 110101010100=>30 110101011000=>21 110101100010=>24 110101100100=>23 110101101000=>22 110101110000=>14 110110001010=>27 110110001100=>17 110110010010=>26 110110010100=>25 110110011000=>16 110110100010=>25 110110100100=>24 110110101000=>23 110110110000=>15 110111000010=>19 110111000100=>18 110111001000=>17 110111010000=>16 110111100000=>9 111000101010=>30 111000101100=>20 111000110010=>22 111000110100=>21 111000111000=>12 111001001010=>29 111001001100=>19 111001010010=>28 111001010100=>27 111001011000=>18 111001100010=>21 111001100100=>20 111001101000=>19 111001110000=>11 111010001010=>28 111010001100=>18 111010010010=>27 111010010100=>26 111010011000=>17 111010100010=>26 111010100100=>25 111010101000=>24 111010110000=>16 111011000010=>20 111011000100=>19 111011001000=>18 111011010000=>17 111011100000=>10 111100001010=>24 111100001100=>14 111100010010=>23 111100010100=>22 111100011000=>13 111100100010=>22 111100100100=>21 111100101000=>20 111100110000=>12 111101000010=>21 111101000100=>20 111101001000=>19 111101010000=>18 111101100000=>11 111110000010=>16 111110000100=>15 111110001000=>14 111110010000=>13 111110100000=>12 111111000000=>6 100001111100=>11 010101010101=>30 010101010011=>20 010101001101=>22 010101001011=>21 010101000111=>12 010100110101=>24 010100110011=>14 010100101101=>23 010100101011=>22 010100100111=>13 010100011101=>16 010100011011=>15 010100010111=>14 010100001111=>6 010011010101=>26 010011010011=>16 010011001101=>18 010011001011=>17 010011000111=>8 010010110101=>25 010010110011=>15 010010101101=>24 010010101011=>23 010010100111=>14 010010011101=>17 010010011011=>16 010010010111=>15 010010001111=>7 010001110101=>20 010001110011=>10 010001101101=>19 010001101011=>18 010001100111=>9 010001011101=>18 010001011011=>17 010001010111=>16 010001001111=>8 010000111101=>12 010000111011=>11 010000110111=>10 010000101111=>9 010000011111=>2 001101010101=>28 001101010011=>18 001101001101=>20 001101001011=>19 001101000111=>10 001100110101=>22 001100110011=>12 001100101101=>21 001100101011=>20 001100100111=>11 001100011101=>14 001100011011=>13 001100010111=>12 001100001111=>4 001011010101=>27 001011010011=>17 001011001101=>19 001011001011=>18 001011000111=>9 001010110101=>26 001010110011=>16 001010101101=>25 001010101011=>24 001010100111=>15 001010011101=>18 001010011011=>17 001010010111=>16 001010001111=>8 001001110101=>21 001001110011=>11 001001101101=>20 001001101011=>19 001001100111=>10 001001011101=>19 001001011011=>18 001001010111=>17 001001001111=>9 001000111101=>13 001000111011=>12 001000110111=>11 001000101111=>10 001000011111=>3 000111010101=>24 000111010011=>14 000111001101=>16 000111001011=>15 000111000111=>6 000110110101=>23 000110110011=>13 000110101101=>22 000110101011=>21 000110100111=>12 000110011101=>15 000110011011=>14 000110010111=>13 000110001111=>5 000101110101=>22 000101110011=>12 000101101101=>21 000101101011=>20 000101100111=>11 000101011101=>20 000101011011=>19 000101010111=>18 000101001111=>10 000100111101=>14 000100111011=>13 000100110111=>12 000100101111=>11 000100011111=>4 000011110101=>18 000011110011=>8 000011101101=>17 000011101011=>16 000011100111=>7 000011011101=>16 000011011011=>15 000011010111=>14 000011001111=>6 000010111101=>15 000010111011=>14 000010110111=>13 000010101111=>12 000010011111=>5 000001111101=>10 000001111011=>9 000001110111=>8 000001101111=>7 000001011111=>6 000000111111=>0 111110000001=>5 111001100001=>10 111000011001=>12 111000110001=>11 111000100101=>20 111011000001=>9 111010010001=>16 111010000101=>18 100111100001=>8 100110011001=>15 100110110001=>14 100110100101=>23 101101100001=>12 101100011001=>14 101100110001=>13 101100100101=>22 101111000001=>7 101110010001=>14 101110000101=>16 101001011001=>19 101001110001=>12 101001100101=>21 101011010001=>18 101011000101=>20 101010010101=>27 000001111110=>11 000111100110=>18 000111111000=>9 000111110010=>19 000111001110=>17 000111011010=>26 000101101110=>22 000101111010=>24 011001100110=>21 011001111000=>12 011001110010=>22 011001011010=>29 011110000110=>16 011110011000=>14 011110010010=>24 011111100000=>7 011111001000=>15 011111000010=>17 011100100110=>22 011100111000=>13 011100110010=>23 011100011010=>24 011101101000=>20 011101100010=>22 011101001010=>30 010011111000=>11 010011110010=>21 010011011010=>28 010001111010=>22 010110100110=>25 010110111000=>16 010110110010=>26 010110011010=>27 010111101000=>18 010111100010=>20 010111001010=>28 010101101010=>33 010101010110=>31 010101011001=>21 010101011010=>32 010101011100=>22 010101100101=>23 010101100110=>24 010101101001=>22 010101101100=>23 010101110001=>14 010101110010=>25 010101110100=>24 010101111000=>15 010110010101=>25 010110010110=>26 010110011001=>16 010110011100=>17 010110100101=>24 010110101001=>23 010110101010=>34 010110101100=>24 010110110001=>15 010110110100=>25 010111000101=>18 010111000110=>19 010111001001=>17 010111001100=>18 010111010001=>16 010111010010=>27 010111010100=>26 010111011000=>17 010111100001=>9 010111100100=>19 010111110000=>10 011001010101=>27 011001010110=>28 011001011001=>18 011001011100=>19 011001100101=>20 011001101001=>19 011001101010=>30 011001101100=>20 011001110001=>11 011001110100=>21 011010010101=>26 011010010110=>27 011010011001=>17 011010011010=>28 011010011100=>18 011010100101=>25 011010100110=>26 011010101001=>24 011010101010=>35 011010101100=>25 011010110001=>16 011010110010=>27 011010110100=>26 011010111000=>17 011011000101=>19 011011000110=>20 011011001001=>18 011011001010=>29 011011001100=>19 011011010001=>17 011011010010=>28 011011010100=>27 011011011000=>18 011011100001=>10 011011100010=>21 011011100100=>20 011011101000=>19 011011110000=>11 011100010101=>22 011100010110=>23 011100011001=>13 011100011100=>14 011100100101=>21 011100101001=>20 011100101010=>31 011100101100=>21 011100110001=>12 011100110100=>22 011101000101=>20 011101000110=>21 011101001001=>19 011101001100=>20 011101010001=>18 011101010010=>29 011101010100=>28 011101011000=>19 011101100001=>11 011101100100=>21 011101110000=>12 011110000101=>15 011110001001=>14 011110001010=>25 011110001100=>15 011110010001=>13 011110010100=>23 011110100001=>12 011110100010=>23 011110100100=>22 011110101000=>21 011110110000=>13 011111000001=>6 011111000100=>16 011111010000=>14 001111000110=>17 001111001010=>26 100111001100=>17 001111001100=>16 001011010110=>28 001111010010=>25 100111010100=>25 001111010100=>24 000111010110=>25 001011011010=>29 100111011000=>16 001111011000=>15 100011011100=>17 010011011100=>18 001011011100=>19 000111011100=>16 000011011110=>17 001101100110=>22 001101101010=>31 100101101100=>22 001101101100=>21 001011100110=>21 001111100010=>18 100111100100=>18 001111100100=>17 010011101010=>29 001011101010=>30 100111101000=>17 001111101000=>16 000111101010=>27 100011101100=>18 010011101100=>19 001011101100=>20 000111101100=>17 000011101110=>18 101001110100=>22 001001110110=>22 001101110010=>23 100101110100=>23 001101110100=>22 000101110110=>23 001011110010=>22 100111110000=>9 001111110000=>8 100011110100=>19 010011110100=>20 001011110100=>21 000111110100=>18 000011110110=>19 110001111000=>11 101001111000=>13 001001111010=>23 100101111000=>14 001101111000=>13 100011111000=>10 001011111000=>12 000011111010=>20 010001111100=>12 001001111100=>13 000101111100=>14 000011111100=>10 100101010101=>29 100101011001=>20 100101100101=>22 100101101001=>21 100101110001=>13 100110010101=>24 100110101001=>22 100111000101=>17 100111001001=>16 100111010001=>15 101001010101=>28 101001101001=>20 101010011001=>18 101010100101=>26 101010101001=>25 101010110001=>17 101011001001=>19 101011100001=>11 101100010101=>23 101100101001=>21 101101000101=>21 101101001001=>20 101101010001=>19 101110001001=>15 101110100001=>13 110001010101=>26 110001011001=>17 110001100101=>19 110001101001=>18 110001110001=>10 110010010101=>25 110010011001=>16 110010100101=>24 110010101001=>23 110010110001=>15 110011000101=>18 110011001001=>17 110011010001=>16 110011100001=>9 110100010101=>24 110100011001=>15 110100100101=>23 110100101001=>22 110100110001=>14 110101000101=>22 110101001001=>21 110101010001=>20 110101100001=>13 110110000101=>17 110110001001=>16 110110010001=>15 110110100001=>14 110111000001=>8 111000010101=>21 111000101001=>19 111001000101=>19 111001001001=>18 111001010001=>17 111010001001=>17 111010100001=>15 111100000101=>14 111100001001=>13 111100010001=>12 111100100001=>11 111101000001=>10 10110111100000=>14 10111011010000=>24 10111011100000=>15 10111100110000=>17 10111101001000=>26 10111101010000=>25 10111101100000=>16 10111110000100=>20 10111110001000=>19 10111110010000=>18 10111110100000=>17 10111111000000=>9 11001111100000=>11 11011110000010=>22 11101101000010=>30 11101110000010=>23 11110011000010=>25 11110100100010=>32 11110101000010=>31 11110110000010=>24 11111000001100=>17 11111000010010=>28 11111000100010=>27 11111001000010=>26 11111010000010=>25 11111100000010=>19 1011110111000000=>17 1011111010100000=>28 1011111011000000=>18 1011111100010000=>21 1011111100100000=>20 1011111101000000=>19 1011111110000000=>10 1111011100000010=>27 1111101010000010=>36 1111101100000010=>28 1111110001000010=>31 1111110010000010=>30 1111110100000010=>29 1111111000000010=>22 111111110000000010=>25 101111111100000000=>11 111111101000000010=>33 101111111010000000=>21 111111100100000010=>34 111111011000000010=>32 101111111001000000=>22 101111110110000000=>20 11111111100000000010=>28 10111111111000000000=>12 11111111010000000010=>37 10111111110100000000=>23 1111111111000000000010=>31 1011111111110000000000=>13
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Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Code
def statistic(x):
    return x.major_index()

Created
Nov 19, 2015 at 11:57 by Martin Rubey
Updated
Nov 17, 2019 at 18:31 by Martin Rubey