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Identifier
Values
=>
0=>1 1=>7 00=>2 01=>5 10=>8 11=>16 000=>3 001=>19 010=>6 011=>14 100=>9 101=>9 110=>17 111=>17 0000=>4 0001=>12 0010=>20 0011=>20 0100=>7 0101=>7 0110=>15 0111=>15 1000=>10 1001=>23 1010=>10 1011=>111 1100=>18 1101=>18 1110=>18 1111=>106 00000=>5 00001=>26 00010=>13 00011=>13 00100=>21 00101=>21 00110=>21 00111=>34 01000=>8 01001=>109 01010=>8 01011=>29 01100=>16 01101=>16 01110=>16 01111=>104 10000=>11 10001=>24 10010=>24 10011=>24 10100=>11 10101=>11 10110=>112 10111=>112 11000=>19 11001=>32 11010=>19 11011=>32 11100=>19 11101=>19 11110=>107 11111=>107 000000=>6 000001=>27 000010=>27 000011=>27 000100=>14 000101=>14 000110=>14 000111=>102 001000=>22 001001=>115 001010=>22 001011=>14 001100=>22 001101=>22 001110=>35 001111=>35 010000=>9 010001=>22 010010=>110 010011=>110 010100=>9 010101=>9 010110=>30 010111=>30 011000=>17 011001=>30 011010=>17 011011=>92 011100=>17 011101=>17 011110=>105 011111=>105 100000=>12 100001=>118 100010=>25 100011=>25 100100=>25 100101=>25 100110=>25 100111=>87 101000=>12 101001=>38 101010=>12 101011=>100 101100=>113 101101=>113 101110=>113 101111=>69 110000=>20 110001=>12 110010=>33 110011=>33 110100=>20 110101=>20 110110=>33 110111=>33 111000=>20 111001=>95 111010=>20 111011=>46 111100=>108 111101=>108 111110=>108 111111=>46 0000000=>7 0000001=>121 0000010=>28 0000011=>28 0000100=>28 0000101=>28 0000110=>28 0000111=>41 0001000=>15 0001001=>90 0001010=>15 0001011=>41 0001100=>15 0001101=>15 0001110=>103 0001111=>103 0010000=>23 0010001=>116 0010010=>116 0010011=>116 0010100=>23 0010101=>23 0010110=>15 0010111=>15 0011000=>23 0011001=>36 0011010=>23 0011011=>85 0011100=>36 0011101=>36 0011110=>36 0011111=>54 0100000=>10 0100001=>98 0100010=>23 0100011=>23 0100100=>111 0100101=>111 0100110=>111 0100111=>67 0101000=>10 0101001=>49 0101010=>10 0101011=>124 0101100=>31 0101101=>31 0101110=>31 0101111=>80 0110000=>18 0110001=>31 0110010=>31 0110011=>31 0110100=>18 0110101=>18 0110110=>93 0110111=>93 0111000=>18 0111001=>44 0111010=>18 0111011=>44 0111100=>106 0111101=>106 0111110=>106 0111111=>44 1000000=>13 1000001=>119 1000010=>119 1000011=>119 1000100=>26 1000101=>26 1000110=>26 1000111=>119 1001000=>26 1001001=>18 1001010=>26 1001011=>39 1001100=>26 1001101=>26 1001110=>88 1001111=>88 1010000=>13 1010001=>39 1010010=>39 1010011=>39 1010100=>13 1010101=>13 1010110=>101 1010111=>101 1011000=>114 1011001=>26 1011010=>114 1011011=>52 1011100=>114 1011101=>114 1011110=>70 1011111=>70 1100000=>21 1100001=>52 1100010=>13 1100011=>13 1100100=>34 1100101=>34 1100110=>34 1100111=>127 1101000=>21 1101001=>83 1101010=>21 1101011=>127 1101100=>34 1101101=>34 1101110=>34 1101111=>52 1110000=>21 1110001=>21 1110010=>96 1110011=>96 1110100=>21 1110101=>21 1110110=>47 1110111=>47 1111000=>109 1111001=>47 1111010=>109 1111011=>65 1111100=>109 1111101=>109 1111110=>47 1111111=>47 00000000=>8 00000001=>122 00000010=>122 00000011=>122 00000100=>29 00000101=>29 00000110=>29 00000111=>78 00001000=>29 00001001=>122 00001010=>29 00001011=>21 00001100=>29 00001101=>29 00001110=>42 00001111=>42 00010000=>16 00010001=>29 00010010=>91 00010011=>91 00010100=>16 00010101=>16 00010110=>42 00010111=>42 00011000=>16 00011001=>42 00011010=>16 00011011=>60 00011100=>104 00011101=>104 00011110=>104 00011111=>42 00100000=>24 00100001=>29 00100010=>117 00100011=>117 00100100=>117 00100101=>117 00100110=>117 00100111=>55 00101000=>24 00101001=>73 00101010=>24 00101011=>117 00101100=>16 00101101=>16 00101110=>16 00101111=>42 00110000=>24 00110001=>37 00110010=>37 00110011=>37 00110100=>24 00110101=>24 00110110=>86 00110111=>86 00111000=>37 00111001=>130 00111010=>37 00111011=>37 00111100=>37 00111101=>37 00111110=>55 00111111=>55 01000000=>11 01000001=>24 01000010=>99 01000011=>99 01000100=>24 01000101=>24 01000110=>24 01000111=>143 01001000=>112 01001001=>50 01001010=>112 01001011=>24 01001100=>112 01001101=>112 01001110=>68 01001111=>68 01010000=>11 01010001=>112 01010010=>50 01010011=>50 01010100=>11 01010101=>11 01010110=>125 01010111=>125 01011000=>32 01011001=>125 01011010=>32 01011011=>125 01011100=>32 01011101=>32 01011110=>81 01011111=>81 01100000=>19 01100001=>125 01100010=>32 01100011=>32 01100100=>32 01100101=>32 01100110=>32 01100111=>50 01101000=>19 01101001=>45 01101010=>19 01101011=>45 01101100=>94 01101101=>94 01101110=>94 01101111=>45 01110000=>19 01110001=>19 01110010=>45 01110011=>45 01110100=>19 01110101=>19 01110110=>45 01110111=>45 01111000=>107 01111001=>63 01111010=>107 01111011=>58 01111100=>107 01111101=>107 01111110=>45 01111111=>45 10000000=>14 10000001=>32 10000010=>120 10000011=>120 10000100=>120 10000101=>120 10000110=>120 10000111=>120 10001000=>27 10001001=>58 10001010=>27 10001011=>76 10001100=>27 10001101=>27 10001110=>120 10001111=>120 10010000=>27 10010001=>19 10010010=>19 10010011=>19 10010100=>27 10010101=>27 10010110=>40 10010111=>40 10011000=>27 10011001=>40 10011010=>27 10011011=>133 10011100=>89 10011101=>89 10011110=>89 10011111=>133 10100000=>14 10100001=>133 10100010=>40 10100011=>40 10100100=>40 10100101=>40 10100110=>40 10100111=>32 10101000=>14 10101001=>58 10101010=>14 10101011=>53 10101100=>102 10101101=>102 10101110=>102 10101111=>40 10110000=>115 10110001=>27 10110010=>27 10110011=>27 10110100=>115 10110101=>115 10110110=>53 10110111=>53 10111000=>115 10111001=>27 10111010=>115 10111011=>53 10111100=>71 10111101=>71 10111110=>71 10111111=>97 11000000=>22 11000001=>115 11000010=>53 11000011=>53 11000100=>14 11000101=>14 11000110=>14 11000111=>40 11001000=>35 11001001=>128 11001010=>35 11001011=>128 11001100=>35 11001101=>35 11001110=>128 11001111=>128 11010000=>22 11010001=>35 11010010=>84 11010011=>84 11010100=>22 11010101=>22 11010110=>128 11010111=>128 11011000=>35 11011001=>35 11011010=>35 11011011=>27 11011100=>35 11011101=>35 11011110=>53 11011111=>53 11100000=>22 11100001=>48 11100010=>22 11100011=>22 11100100=>97 11100101=>97 11100110=>97 11100111=>141 11101000=>22 11101001=>48 11101010=>22 11101011=>141 11101100=>48 11101101=>48 11101110=>48 11101111=>97 11110000=>110 11110001=>22 11110010=>48 11110011=>48 11110100=>110 11110101=>110 11110110=>66 11110111=>66 11111000=>110 11111001=>61 11111010=>110 11111011=>35 11111100=>48 11111101=>48 11111110=>48 11111111=>61 000000000=>9 000000001=>35 000000010=>123 000000011=>123 000000100=>123 000000101=>123 000000110=>123 000000111=>61 000001000=>30 000001001=>123 000001010=>30 000001011=>123 000001100=>30 000001101=>30 000001110=>79 000001111=>79 000010000=>30 000010001=>30 000010010=>123 000010011=>123 000010100=>30 000010101=>30 000010110=>22 000010111=>22 000011000=>30 000011001=>22 000011010=>30 000011011=>48 000011100=>43 000011101=>43 000011110=>43 000011111=>136 000100000=>17 000100001=>43 000100010=>30 000100011=>30 000100100=>92 000100101=>92 000100110=>92 000100111=>43 000101000=>17 000101001=>136 000101010=>17 000101011=>30 000101100=>43 000101101=>43 000101110=>43 000101111=>87 000110000=>17 000110001=>43 000110010=>43 000110011=>43 000110100=>17 000110101=>17 000110110=>61 000110111=>61 000111000=>105 000111001=>56 000111010=>105 000111011=>30 000111100=>105 000111101=>105 000111110=>43 000111111=>43 001000000=>25 001000001=>30 001000010=>30 001000011=>30 001000100=>118 001000101=>118 001000110=>118 001000111=>30 001001000=>118 001001001=>56 001001010=>118 001001011=>118 001001100=>118 001001101=>118 001001110=>56 001001111=>56 001010000=>25 001010001=>74 001010010=>74 001010011=>74 001010100=>25 001010101=>25 001010110=>118 001010111=>118 001011000=>17 001011001=>56 001011010=>17 001011011=>69 001011100=>17 001011101=>17 001011110=>43 001011111=>43 001100000=>25 001100001=>131 001100010=>38 001100011=>38 001100100=>38 001100101=>38 001100110=>38 001100111=>69 001101000=>25 001101001=>131 001101010=>25 001101011=>131 001101100=>87 001101101=>87 001101110=>87 001101111=>131 001110000=>38 001110001=>25 001110010=>131 001110011=>131 001110100=>38 001110101=>38 001110110=>38 001110111=>38 001111000=>38 001111001=>30 001111010=>38 001111011=>30 001111100=>56 001111101=>56 001111110=>56 001111111=>131 010000000=>12 010000001=>51 010000010=>25 010000011=>25 010000100=>100 010000101=>100 010000110=>100 010000111=>38 010001000=>25 010001001=>144 010001010=>25 010001011=>100 010001100=>25 010001101=>25 010001110=>144 010001111=>144 010010000=>113 010010001=>51 010010010=>51 010010011=>51 010010100=>113 010010101=>113 010010110=>25 010010111=>25 010011000=>113 010011001=>51 010011010=>113 010011011=>144 010011100=>69 010011101=>69 010011110=>69 010011111=>95 010100000=>12 010100001=>64 010100010=>113 010100011=>113 010100100=>51 010100101=>51 010100110=>51 010100111=>64 010101000=>12 010101001=>64 010101010=>12 010101011=>38 010101100=>126 010101101=>126 010101110=>126 010101111=>38 010110000=>33 010110001=>126 010110010=>126 010110011=>126 010110100=>33 010110101=>33 010110110=>126 010110111=>126 010111000=>33 010111001=>126 010111010=>33 010111011=>64 010111100=>82 010111101=>82 010111110=>82 010111111=>170 011000000=>20 011000001=>33 011000010=>126 011000011=>126 011000100=>33 011000101=>33 011000110=>33 011000111=>64 011001000=>33 011001001=>25 011001010=>33 011001011=>25 011001100=>33 011001101=>33 011001110=>51 011001111=>51 011010000=>20 011010001=>46 011010010=>46 011010011=>46 011010100=>20 011010101=>20 011010110=>46 011010111=>46 011011000=>95 011011001=>33 011011010=>95 011011011=>139 011011100=>95 011011101=>95 011011110=>46 011011111=>46 011100000=>20 011100001=>139 011100010=>20 011100011=>20 011100100=>46 011100101=>46 011100110=>46 011100111=>95 011101000=>20 011101001=>90 011101010=>20 011101011=>46 011101100=>46 011101101=>46 011101110=>46 011101111=>139 011110000=>108 011110001=>20 011110010=>64 011110011=>64 011110100=>108 011110101=>108 011110110=>59 011110111=>59 011111000=>108 011111001=>33 011111010=>108 011111011=>152 011111100=>46 011111101=>46 011111110=>46 011111111=>59 100000000=>15 100000001=>33 100000010=>33 100000011=>33 100000100=>121 100000101=>121 100000110=>121 100000111=>152 100001000=>121 100001001=>33 100001010=>121 100001011=>59 100001100=>121 100001101=>121 100001110=>121 100001111=>121 100010000=>28 100010001=>121 100010010=>59 100010011=>59 100010100=>28 100010101=>28 100010110=>77 100010111=>77 100011000=>28 100011001=>77 100011010=>28 100011011=>103 100011100=>121 100011101=>121 100011110=>121 100011111=>72 100100000=>28 100100001=>59 100100010=>20 100100011=>20 100100100=>20 100100101=>20 100100110=>20 100100111=>72 100101000=>28 100101001=>46 100101010=>28 100101011=>134 100101100=>41 100101101=>41 100101110=>41 100101111=>134 100110000=>28 100110001=>41 100110010=>41 100110011=>41 100110100=>28 100110101=>28 100110110=>134 100110111=>134 100111000=>90 100111001=>134 100111010=>90 100111011=>41 100111100=>90 100111101=>90 100111110=>134 100111111=>134 101000000=>15 101000001=>28 101000010=>134 101000011=>134 101000100=>41 101000101=>41 101000110=>41 101000111=>85 101001000=>41 101001001=>41 101001010=>41 101001011=>41 101001100=>41 101001101=>41 101001110=>33 101001111=>33 101010000=>15 101010001=>59 101010010=>59 101010011=>59 101010100=>15 101010101=>15 101010110=>54 101010111=>54 101011000=>103 101011001=>28 101011010=>103 101011011=>147 101011100=>103 101011101=>103 101011110=>41 101011111=>41 101100000=>116 101100001=>147 101100010=>28 101100011=>28 101100100=>28 101100101=>28 101100110=>28 101100111=>178 101101000=>116 101101001=>147 101101010=>116 101101011=>28 101101100=>54 101101101=>54 101101110=>54 101101111=>147 101110000=>116 101110001=>116 101110010=>28 101110011=>28 101110100=>116 101110101=>116 101110110=>54 101110111=>54 101111000=>72 101111001=>147 101111010=>72 101111011=>46 101111100=>72 101111101=>72 101111110=>98 101111111=>98 110000000=>23 110000001=>67 110000010=>116 110000011=>116 110000100=>54 110000101=>54 110000110=>54 110000111=>116 110001000=>15 110001001=>67 110001010=>15 110001011=>54 110001100=>15 110001101=>15 110001110=>41 110001111=>41 110010000=>36 110010001=>129 110010010=>129 110010011=>129 110010100=>36 110010101=>36 110010110=>129 110010111=>129 110011000=>36 110011001=>129 110011010=>36 110011011=>67 110011100=>129 110011101=>129 110011110=>129 110011111=>116 110100000=>23 110100001=>129 110100010=>36 110100011=>36 110100100=>85 110100101=>85 110100110=>85 110100111=>129 110101000=>23 110101001=>173 110101010=>23 110101011=>85 110101100=>129 110101101=>129 110101110=>129 110101111=>36 110110000=>36 110110001=>36 110110010=>36 110110011=>36 110110100=>36 110110101=>36 110110110=>28 110110111=>28 110111000=>36 110111001=>28 110111010=>36 110111011=>28 110111100=>54 110111101=>54 110111110=>54 110111111=>129 111000000=>23 111000001=>49 111000010=>49 111000011=>49 111000100=>23 111000101=>23 111000110=>23 111000111=>142 111001000=>98 111001001=>49 111001010=>98 111001011=>36 111001100=>98 111001101=>98 111001110=>142 111001111=>142 111010000=>23 111010001=>98 111010010=>49 111010011=>49 111010100=>23 111010101=>23 111010110=>142 111010111=>142 111011000=>49 111011001=>23 111011010=>49 111011011=>36 111011100=>49 111011101=>49 111011110=>98 111011111=>98 111100000=>111 111100001=>93 111100010=>23 111100011=>23 111100100=>49 111100101=>49 111100110=>49 111100111=>49 111101000=>111 111101001=>142 111101010=>111 111101011=>41 111101100=>67 111101101=>67 111101110=>67 111101111=>93 111110000=>111 111110001=>111 111110010=>62 111110011=>62 111110100=>111 111110101=>111 111110110=>36 111110111=>36 111111000=>49 111111001=>155 111111010=>49 111111011=>62 111111100=>49 111111101=>49 111111110=>62 111111111=>62 0000000001=>36 0010000001=>150 0010101101=>119 0010101011=>119 0010100111=>49 0010011101=>57 0010011011=>57 0010010111=>119 0010001111=>31 0001110101=>106 0001110011=>57 0001101101=>62 0001101011=>36 0001100111=>137 0001011101=>44 0001011011=>93 0001010111=>31 0001001111=>44 0000111101=>44 0000111011=>137 0000110111=>49 0000101111=>168 0000011111=>168 0000000000=>10 0000000110=>124 0000011000=>31 0000011110=>80 0000010010=>124 0001100000=>18 0001100110=>44 0001111000=>106 0001111110=>44 0001110010=>57 0001001000=>93 0001001110=>44 0001000010=>44 0001011010=>44 0010101010=>26 0010101000=>26 0010101100=>119 0010100100=>75 0010010100=>119 0001010100=>18 0010101110=>119 0010100000=>26 0010000100=>31 0000010100=>31 0000000010=>36 0000001110=>62 0000111110=>137 0000000100=>124 0000001010=>124 0000010110=>124 0000101110=>23 0001011110=>88 0001101110=>62 0001110110=>31 0001111010=>106 0001111100=>44 0000000101=>124 0000001101=>124 0000011101=>80 0001111101=>44 0000001001=>155 0000010101=>31 0000101101=>23 0010110001=>57 0001100001=>44 0001000001=>44 0000111111=>137 0001110100=>106 0001101100=>62 0010011100=>57 0001011100=>44 0000111100=>44 0001101010=>18 0010011010=>119 0000111010=>44 0010100110=>75 0010010110=>119 0001010110=>31 0000110110=>49 0010001110=>31 0001101001=>36 0000110001=>23 0000010001=>124 0000001100=>124 0000011001=>62 0000110011=>23 0000110100=>31 0000000011=>36 0000011011=>93 0001101111=>62 0000110101=>31 0010000010=>31 0001000011=>44 0010011110=>57 0001010000=>18 0001000100=>31 0001010101=>18 0001001011=>31 0001100011=>44 0001110111=>31 0010000000=>26 0000000111=>36 0000001111=>62 0001111111=>57 0000001011=>124 0000010111=>124 0001011111=>88 0001111001=>150 0000011010=>31 0000101010=>31 0000100101=>124 0010010001=>57 0010000101=>31 0010010101=>119 0010010011=>57 0000101011=>62 0001000111=>75 0000100111=>75 0010010010=>57 0001001010=>93 0001001001=>137 0001000101=>31 0000100011=>31 0000100100=>124 0000100010=>31 0010110000=>18 0000011100=>80 0000001000=>124 0000101100=>23 0010101111=>70 0000101000=>31 0010001000=>119 0001001100=>93 0001000110=>31 0001100100=>44 0001100010=>44 0000100110=>124 0000110010=>23 0010010000=>119 0001010010=>137 0001000000=>18 0001011001=>137 0001100101=>44 0001110001=>18 0010011001=>31 0010100101=>75 0010101001=>101 0010011111=>88 0000111001=>137 0010001101=>119 0001001101=>93 0001010001=>93 0001010011=>137 0001111011=>57 0010011000=>119 0001011000=>44 0000100000=>31 0010001011=>150 0010000111=>57 0000010011=>124 0010001100=>119 0010000110=>31 0000110000=>31 0000100001=>80 0010100011=>75 0010100001=>150 0000111000=>44 0001101000=>18 0000010000=>31 0000101001=>75 0010100010=>75 0010001001=>181 0010000011=>31 0010001010=>119 0001110000=>106
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Description
The stopping time of the decimal representation of the binary word for the 3x+1 problem.
Prepend $1$ to the binary word, interpret it as a positive number, and count the number of halving and tripling steps needed to reach $1$.
References
[1] wikipedia:3x_+_1_problem
Code
def statistic(w):
    return collatz(Integer("0b1" + str(w)))

@cached_function
def collatz(n):
    if n == 1:
        return 0
    elif is_even(n):
        return 1+collatz(n//2)
    else:
        return 1+collatz(3*n+1)
Created
May 30, 2017 at 22:00 by Martin Rubey
Updated
May 30, 2017 at 22:00 by Martin Rubey