*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000826
-----------------------------------------------------------------------------
Collection: Binary words
-----------------------------------------------------------------------------
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)
-----------------------------------------------------------------------------
Statistic 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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Created: May 30, 2017 at 22:00 by Martin Rubey
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Last Updated: May 30, 2017 at 22:00 by Martin Rubey