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Identifier
Values
=>
0=>0 1=>1 00=>0 01=>2 10=>1 11=>3 000=>0 001=>3 010=>2 011=>5 100=>1 101=>4 110=>3 111=>6 0000=>0 0001=>4 0010=>3 0011=>7 0100=>2 0101=>6 0110=>5 0111=>9 1000=>1 1001=>5 1010=>4 1011=>8 1100=>3 1101=>7 1110=>6 1111=>10 00000=>0 00001=>5 00010=>4 00011=>9 00100=>3 00101=>8 00110=>7 00111=>12 01000=>2 01001=>7 01010=>6 01011=>11 01100=>5 01101=>10 01110=>9 01111=>14 10000=>1 10001=>6 10010=>5 10011=>10 10100=>4 10101=>9 10110=>8 10111=>13 11000=>3 11001=>8 11010=>7 11011=>12 11100=>6 11101=>11 11110=>10 11111=>15 000000=>0 000001=>6 000010=>5 000011=>11 000100=>4 000101=>10 000110=>9 000111=>15 001000=>3 001001=>9 001010=>8 001011=>14 001100=>7 001101=>13 001110=>12 001111=>18 010000=>2 010001=>8 010010=>7 010011=>13 010100=>6 010101=>12 010110=>11 010111=>17 011000=>5 011001=>11 011010=>10 011011=>16 011100=>9 011101=>15 011110=>14 011111=>20 100000=>1 100001=>7 100010=>6 100011=>12 100100=>5 100101=>11 100110=>10 100111=>16 101000=>4 101001=>10 101010=>9 101011=>15 101100=>8 101101=>14 101110=>13 101111=>19 110000=>3 110001=>9 110010=>8 110011=>14 110100=>7 110101=>13 110110=>12 110111=>18 111000=>6 111001=>12 111010=>11 111011=>17 111100=>10 111101=>16 111110=>15 111111=>21 0000000=>0 0000001=>7 0000010=>6 0000011=>13 0000100=>5 0000101=>12 0000110=>11 0000111=>18 0001000=>4 0001001=>11 0001010=>10 0001011=>17 0001100=>9 0001101=>16 0001110=>15 0001111=>22 0010000=>3 0010001=>10 0010010=>9 0010011=>16 0010100=>8 0010101=>15 0010110=>14 0010111=>21 0011000=>7 0011001=>14 0011010=>13 0011011=>20 0011100=>12 0011101=>19 0011110=>18 0011111=>25 0100000=>2 0100001=>9 0100010=>8 0100011=>15 0100100=>7 0100101=>14 0100110=>13 0100111=>20 0101000=>6 0101001=>13 0101010=>12 0101011=>19 0101100=>11 0101101=>18 0101110=>17 0101111=>24 0110000=>5 0110001=>12 0110010=>11 0110011=>18 0110100=>10 0110101=>17 0110110=>16 0110111=>23 0111000=>9 0111001=>16 0111010=>15 0111011=>22 0111100=>14 0111101=>21 0111110=>20 0111111=>27 1000000=>1 1000001=>8 1000010=>7 1000011=>14 1000100=>6 1000101=>13 1000110=>12 1000111=>19 1001000=>5 1001001=>12 1001010=>11 1001011=>18 1001100=>10 1001101=>17 1001110=>16 1001111=>23 1010000=>4 1010001=>11 1010010=>10 1010011=>17 1010100=>9 1010101=>16 1010110=>15 1010111=>22 1011000=>8 1011001=>15 1011010=>14 1011011=>21 1011100=>13 1011101=>20 1011110=>19 1011111=>26 1100000=>3 1100001=>10 1100010=>9 1100011=>16 1100100=>8 1100101=>15 1100110=>14 1100111=>21 1101000=>7 1101001=>14 1101010=>13 1101011=>20 1101100=>12 1101101=>19 1101110=>18 1101111=>25 1110000=>6 1110001=>13 1110010=>12 1110011=>19 1110100=>11 1110101=>18 1110110=>17 1110111=>24 1111000=>10 1111001=>17 1111010=>16 1111011=>23 1111100=>15 1111101=>22 1111110=>21 1111111=>28 00000000=>0 00000001=>8 00000010=>7 00000011=>15 00000100=>6 00000101=>14 00000110=>13 00000111=>21 00001000=>5 00001001=>13 00001010=>12 00001011=>20 00001100=>11 00001101=>19 00001110=>18 00001111=>26 00010000=>4 00010001=>12 00010010=>11 00010011=>19 00010100=>10 00010101=>18 00010110=>17 00010111=>25 00011000=>9 00011001=>17 00011010=>16 00011011=>24 00011100=>15 00011101=>23 00011110=>22 00011111=>30 00100000=>3 00100001=>11 00100010=>10 00100011=>18 00100100=>9 00100101=>17 00100110=>16 00100111=>24 00101000=>8 00101001=>16 00101010=>15 00101011=>23 00101100=>14 00101101=>22 00101110=>21 00101111=>29 00110000=>7 00110001=>15 00110010=>14 00110011=>22 00110100=>13 00110101=>21 00110110=>20 00110111=>28 00111000=>12 00111001=>20 00111010=>19 00111011=>27 00111100=>18 00111101=>26 00111110=>25 00111111=>33 01000000=>2 01000001=>10 01000010=>9 01000011=>17 01000100=>8 01000101=>16 01000110=>15 01000111=>23 01001000=>7 01001001=>15 01001010=>14 01001011=>22 01001100=>13 01001101=>21 01001110=>20 01001111=>28 01010000=>6 01010001=>14 01010010=>13 01010011=>21 01010100=>12 01010101=>20 01010110=>19 01010111=>27 01011000=>11 01011001=>19 01011010=>18 01011011=>26 01011100=>17 01011101=>25 01011110=>24 01011111=>32 01100000=>5 01100001=>13 01100010=>12 01100011=>20 01100100=>11 01100101=>19 01100110=>18 01100111=>26 01101000=>10 01101001=>18 01101010=>17 01101011=>25 01101100=>16 01101101=>24 01101110=>23 01101111=>31 01110000=>9 01110001=>17 01110010=>16 01110011=>24 01110100=>15 01110101=>23 01110110=>22 01110111=>30 01111000=>14 01111001=>22 01111010=>21 01111011=>29 01111100=>20 01111101=>28 01111110=>27 01111111=>35 10000000=>1 10000001=>9 10000010=>8 10000011=>16 10000100=>7 10000101=>15 10000110=>14 10000111=>22 10001000=>6 10001001=>14 10001010=>13 10001011=>21 10001100=>12 10001101=>20 10001110=>19 10001111=>27 10010000=>5 10010001=>13 10010010=>12 10010011=>20 10010100=>11 10010101=>19 10010110=>18 10010111=>26 10011000=>10 10011001=>18 10011010=>17 10011011=>25 10011100=>16 10011101=>24 10011110=>23 10011111=>31 10100000=>4 10100001=>12 10100010=>11 10100011=>19 10100100=>10 10100101=>18 10100110=>17 10100111=>25 10101000=>9 10101001=>17 10101010=>16 10101011=>24 10101100=>15 10101101=>23 10101110=>22 10101111=>30 10110000=>8 10110001=>16 10110010=>15 10110011=>23 10110100=>14 10110101=>22 10110110=>21 10110111=>29 10111000=>13 10111001=>21 10111010=>20 10111011=>28 10111100=>19 10111101=>27 10111110=>26 10111111=>34 11000000=>3 11000001=>11 11000010=>10 11000011=>18 11000100=>9 11000101=>17 11000110=>16 11000111=>24 11001000=>8 11001001=>16 11001010=>15 11001011=>23 11001100=>14 11001101=>22 11001110=>21 11001111=>29 11010000=>7 11010001=>15 11010010=>14 11010011=>22 11010100=>13 11010101=>21 11010110=>20 11010111=>28 11011000=>12 11011001=>20 11011010=>19 11011011=>27 11011100=>18 11011101=>26 11011110=>25 11011111=>33 11100000=>6 11100001=>14 11100010=>13 11100011=>21 11100100=>12 11100101=>20 11100110=>19 11100111=>27 11101000=>11 11101001=>19 11101010=>18 11101011=>26 11101100=>17 11101101=>25 11101110=>24 11101111=>32 11110000=>10 11110001=>18 11110010=>17 11110011=>25 11110100=>16 11110101=>24 11110110=>23 11110111=>31 11111000=>15 11111001=>23 11111010=>22 11111011=>30 11111100=>21 11111101=>29 11111110=>28 11111111=>36 000000000=>0 000000001=>9 000000010=>8 000000011=>17 000000100=>7 000000101=>16 000000110=>15 000000111=>24 000001000=>6 000001001=>15 000001010=>14 000001011=>23 000001100=>13 000001101=>22 000001110=>21 000001111=>30 000010000=>5 000010001=>14 000010010=>13 000010011=>22 000010100=>12 000010101=>21 000010110=>20 000010111=>29 000011000=>11 000011001=>20 000011010=>19 000011011=>28 000011100=>18 000011101=>27 000011110=>26 000011111=>35 000100000=>4 000100001=>13 000100010=>12 000100011=>21 000100100=>11 000100101=>20 000100110=>19 000100111=>28 000101000=>10 000101001=>19 000101010=>18 000101011=>27 000101100=>17 000101101=>26 000101110=>25 000101111=>34 000110000=>9 000110001=>18 000110010=>17 000110011=>26 000110100=>16 000110101=>25 000110110=>24 000110111=>33 000111000=>15 000111001=>24 000111010=>23 000111011=>32 000111100=>22 000111101=>31 000111110=>30 000111111=>39 001000000=>3 001000001=>12 001000010=>11 001000011=>20 001000100=>10 001000101=>19 001000110=>18 001000111=>27 001001000=>9 001001001=>18 001001010=>17 001001011=>26 001001100=>16 001001101=>25 001001110=>24 001001111=>33 001010000=>8 001010001=>17 001010010=>16 001010011=>25 001010100=>15 001010101=>24 001010110=>23 001010111=>32 001011000=>14 001011001=>23 001011010=>22 001011011=>31 001011100=>21 001011101=>30 001011110=>29 001011111=>38 001100000=>7 001100001=>16 001100010=>15 001100011=>24 001100100=>14 001100101=>23 001100110=>22 001100111=>31 001101000=>13 001101001=>22 001101010=>21 001101011=>30 001101100=>20 001101101=>29 001101110=>28 001101111=>37 001110000=>12 001110001=>21 001110010=>20 001110011=>29 001110100=>19 001110101=>28 001110110=>27 001110111=>36 001111000=>18 001111001=>27 001111010=>26 001111011=>35 001111100=>25 001111101=>34 001111110=>33 001111111=>42 010000000=>2 010000001=>11 010000010=>10 010000011=>19 010000100=>9 010000101=>18 010000110=>17 010000111=>26 010001000=>8 010001001=>17 010001010=>16 010001011=>25 010001100=>15 010001101=>24 010001110=>23 010001111=>32 010010000=>7 010010001=>16 010010010=>15 010010011=>24 010010100=>14 010010101=>23 010010110=>22 010010111=>31 010011000=>13 010011001=>22 010011010=>21 010011011=>30 010011100=>20 010011101=>29 010011110=>28 010011111=>37 010100000=>6 010100001=>15 010100010=>14 010100011=>23 010100100=>13 010100101=>22 010100110=>21 010100111=>30 010101000=>12 010101001=>21 010101010=>20 010101011=>29 010101100=>19 010101101=>28 010101110=>27 010101111=>36 010110000=>11 010110001=>20 010110010=>19 010110011=>28 010110100=>18 010110101=>27 010110110=>26 010110111=>35 010111000=>17 010111001=>26 010111010=>25 010111011=>34 010111100=>24 010111101=>33 010111110=>32 010111111=>41 011000000=>5 011000001=>14 011000010=>13 011000011=>22 011000100=>12 011000101=>21 011000110=>20 011000111=>29 011001000=>11 011001001=>20 011001010=>19 011001011=>28 011001100=>18 011001101=>27 011001110=>26 011001111=>35 011010000=>10 011010001=>19 011010010=>18 011010011=>27 011010100=>17 011010101=>26 011010110=>25 011010111=>34 011011000=>16 011011001=>25 011011010=>24 011011011=>33 011011100=>23 011011101=>32 011011110=>31 011011111=>40 011100000=>9 011100001=>18 011100010=>17 011100011=>26 011100100=>16 011100101=>25 011100110=>24 011100111=>33 011101000=>15 011101001=>24 011101010=>23 011101011=>32 011101100=>22 011101101=>31 011101110=>30 011101111=>39 011110000=>14 011110001=>23 011110010=>22 011110011=>31 011110100=>21 011110101=>30 011110110=>29 011110111=>38 011111000=>20 011111001=>29 011111010=>28 011111011=>37 011111100=>27 011111101=>36 011111110=>35 011111111=>44 100000000=>1 100000001=>10 100000010=>9 100000011=>18 100000100=>8 100000101=>17 100000110=>16 100000111=>25 100001000=>7 100001001=>16 100001010=>15 100001011=>24 100001100=>14 100001101=>23 100001110=>22 100001111=>31 100010000=>6 100010001=>15 100010010=>14 100010011=>23 100010100=>13 100010101=>22 100010110=>21 100010111=>30 100011000=>12 100011001=>21 100011010=>20 100011011=>29 100011100=>19 100011101=>28 100011110=>27 100011111=>36 100100000=>5 100100001=>14 100100010=>13 100100011=>22 100100100=>12 100100101=>21 100100110=>20 100100111=>29 100101000=>11 100101001=>20 100101010=>19 100101011=>28 100101100=>18 100101101=>27 100101110=>26 100101111=>35 100110000=>10 100110001=>19 100110010=>18 100110011=>27 100110100=>17 100110101=>26 100110110=>25 100110111=>34 100111000=>16 100111001=>25 100111010=>24 100111011=>33 100111100=>23 100111101=>32 100111110=>31 100111111=>40 101000000=>4 101000001=>13 101000010=>12 101000011=>21 101000100=>11 101000101=>20 101000110=>19 101000111=>28 101001000=>10 101001001=>19 101001010=>18 101001011=>27 101001100=>17 101001101=>26 101001110=>25 101001111=>34 101010000=>9 101010001=>18 101010010=>17 101010011=>26 101010100=>16 101010101=>25 101010110=>24 101010111=>33 101011000=>15 101011001=>24 101011010=>23 101011011=>32 101011100=>22 101011101=>31 101011110=>30 101011111=>39 101100000=>8 101100001=>17 101100010=>16 101100011=>25 101100100=>15 101100101=>24 101100110=>23 101100111=>32 101101000=>14 101101001=>23 101101010=>22 101101011=>31 101101100=>21 101101101=>30 101101110=>29 101101111=>38 101110000=>13 101110001=>22 101110010=>21 101110011=>30 101110100=>20 101110101=>29 101110110=>28 101110111=>37 101111000=>19 101111001=>28 101111010=>27 101111011=>36 101111100=>26 101111101=>35 101111110=>34 101111111=>43 110000000=>3 110000001=>12 110000010=>11 110000011=>20 110000100=>10 110000101=>19 110000110=>18 110000111=>27 110001000=>9 110001001=>18 110001010=>17 110001011=>26 110001100=>16 110001101=>25 110001110=>24 110001111=>33 110010000=>8 110010001=>17 110010010=>16 110010011=>25 110010100=>15 110010101=>24 110010110=>23 110010111=>32 110011000=>14 110011001=>23 110011010=>22 110011011=>31 110011100=>21 110011101=>30 110011110=>29 110011111=>38 110100000=>7 110100001=>16 110100010=>15 110100011=>24 110100100=>14 110100101=>23 110100110=>22 110100111=>31 110101000=>13 110101001=>22 110101010=>21 110101011=>30 110101100=>20 110101101=>29 110101110=>28 110101111=>37 110110000=>12 110110001=>21 110110010=>20 110110011=>29 110110100=>19 110110101=>28 110110110=>27 110110111=>36 110111000=>18 110111001=>27 110111010=>26 110111011=>35 110111100=>25 110111101=>34 110111110=>33 110111111=>42 111000000=>6 111000001=>15 111000010=>14 111000011=>23 111000100=>13 111000101=>22 111000110=>21 111000111=>30 111001000=>12 111001001=>21 111001010=>20 111001011=>29 111001100=>19 111001101=>28 111001110=>27 111001111=>36 111010000=>11 111010001=>20 111010010=>19 111010011=>28 111010100=>18 111010101=>27 111010110=>26 111010111=>35 111011000=>17 111011001=>26 111011010=>25 111011011=>34 111011100=>24 111011101=>33 111011110=>32 111011111=>41 111100000=>10 111100001=>19 111100010=>18 111100011=>27 111100100=>17 111100101=>26 111100110=>25 111100111=>34 111101000=>16 111101001=>25 111101010=>24 111101011=>33 111101100=>23 111101101=>32 111101110=>31 111101111=>40 111110000=>15 111110001=>24 111110010=>23 111110011=>32 111110100=>22 111110101=>31 111110110=>30 111110111=>39 111111000=>21 111111001=>30 111111010=>29 111111011=>38 111111100=>28 111111101=>37 111111110=>36 111111111=>45 0000000001=>10 0010000001=>13 0010101101=>33 0010101011=>34 0010100111=>35 0010011101=>34 0010011011=>35 0010010111=>36 0010001111=>37 0001110101=>33 0001110011=>34 0001101101=>34 0001101011=>35 0001100111=>36 0001011101=>35 0001011011=>36 0001010111=>37 0001001111=>38 0000111101=>36 0000111011=>37 0000110111=>38 0000101111=>39 0000011111=>40 0000000000=>0 0000000110=>17 0000011000=>13 0000011110=>30 0000010010=>15 0001100000=>9 0001100110=>26 0001111000=>22 0001111110=>39 0001110010=>24 0001001000=>11 0001001110=>28 0001000010=>13 0001011010=>26 0010101010=>24 0010101000=>15 0010101100=>23 0010100100=>16 0010010100=>17 0001010100=>18 0010101110=>32 0010100000=>8 0010000100=>11 0000010100=>14 0000000010=>9 0000001110=>24 0000111110=>35 0000000100=>8 0000001010=>16 0000010110=>23 0000101110=>29 0001011110=>34 0001101110=>33 0001110110=>32 0001111010=>31 0001111100=>30 0000000101=>18 0000001101=>25 0000011101=>31 0001111101=>40 0000001001=>17 0000010101=>24 0000101101=>30 0010110001=>24 0001100001=>19 0001000001=>14 0000111111=>45 0001110100=>23 0001101100=>24 0010011100=>24 0001011100=>25 0000111100=>26 0001101010=>25 0010011010=>25 0000111010=>27 0010100110=>25 0010010110=>26 0001010110=>27 0000110110=>28 0010001110=>27 0001101001=>26 0000110001=>21 0000010001=>16 0000001100=>15 0000011001=>23 0000110011=>30 0000110100=>19 0000000011=>19 0000011011=>32 0001101111=>43 0000110101=>29 0010000010=>12 0001000011=>23 0010011110=>33 0001010000=>10 0001000100=>12 0001010101=>28 0001001011=>30 0001100011=>28 0001110111=>42 0010000000=>3 0000000111=>27 0000001111=>34 0001111111=>49 0000001011=>26 0000010111=>33 0001011111=>44 0001111001=>32 0000011010=>22 0000101010=>21 0000100101=>23 0010010001=>19 0010000101=>21 0010010101=>27 0010010011=>28 0000101011=>31 0001000111=>31 0000100111=>32 0010010010=>18 0001001010=>20 0001001001=>21 0001000101=>22 0000100011=>24 0000100100=>13 0000100010=>14 0010110000=>14 0000011100=>21 0000001000=>7 0000101100=>20 0010101111=>42 0000101000=>12 0010001000=>10 0001001100=>19 0001000110=>21 0001100100=>17 0001100010=>18 0000100110=>22 0000110010=>20 0010010000=>9 0001010010=>19 0001000000=>4 0001011001=>27 0001100101=>27 0001110001=>25 0010011001=>26 0010100101=>26 0010101001=>25 0010011111=>43 0000111001=>28 0010001101=>28 0001001101=>29 0001010001=>20 0001010011=>29 0001111011=>41 0010011000=>16 0001011000=>17 0000100000=>5 0010001011=>29 0010000111=>30 0000010011=>25 0010001100=>18 0010000110=>20 0000110000=>11 0000100001=>15 0010100011=>27 0010100001=>18 0000111000=>18 0001101000=>16 0000010000=>6 0000101001=>22 0010100010=>17 0010001001=>20 0010000011=>22 0010001010=>19 0001110000=>15
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Description
The sum of the positions of the ones in a binary word.
References
[1] Irregular triangle read by rows giving coefficients in expansion of Product_k=1..n (1 + x^k). OEIS:A053632
Code
def statistic(w):
     return sum(i for (i, e) in enumerate(w, 1) if e == 1)

Created
Feb 12, 2016 at 21:50 by Martin Rubey
Updated
Feb 12, 2016 at 21:50 by Martin Rubey