Table 5: Numbers of Predecessors of 6-bit Strings
15, 30, 45, 51, 60, 90, 105, 106, 150, 154, 170, 204
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
37, 164
26 12 9 9 9 3 6 6 9 3 2 2 5 3 4 4
9 3 2 2 2 2 2 2 6 2 2 2 4 2 3 3
12 6 3 3 3 1 2 2 3 1 2 2 3 1 2 2
9 3 2 2 2 2 2 2 6 2 2 2 4 2 3 3
22, 104
29 11 8 8 7 5 6 6 7 3 3 3 6 2 4 4
8 4 2 2 3 1 2 2 6 2 2 2 4 2 3 3
11 5 4 4 3 1 2 2 5 1 1 1 2 2 2 2
8 4 2 2 3 1 2 2 6 2 2 2 4 2 3 3
94, 122
2 2 1 3 0 2 3 3 0 0 2 2 2 4 2 4
1 1 1 1 2 8 5 5 3 3 5 9 2 4 5 9
2 2 1 3 0 2 3 3 2 2 8 8 4 10 4 10
3 3 1 5 2 8 9 9 3 3 5 9 4 10 9 13
73, 146
17 9 8 6 7 7 8 2 7 3 7 3 5 5 1 1
8 6 5 1 7 7 5 1 8 2 5 5 1 1 1 1
9 5 6 4 3 3 2 0 7 3 7 3 5 5 1 1
6 4 1 1 3 3 5 1 2 0 1 1 1 1 1 1
25, 152
10 8 12 2 11 9 2 2 12 6 8 6 3 1 2 2
10 8 8 2 8 4 4 4 3 3 2 0 3 1 2 2
8 6 8 2 7 5 2 2 6 4 4 2 3 1 2 2
4 2 4 2 2 2 0 0 3 3 2 0 3 1 2 2
41
10 8 8 6 8 6 9 1 10 4 6 4 8 6 1 1
9 7 5 3 7 3 4 2 6 6 6 2 2 0 1 1
8 6 6 4 6 4 5 1 6 4 4 2 4 2 1 1
5 3 5 3 3 3 2 0 2 2 0 0 2 0 1 1
134
10 8 9 5 10 6 6 2 8 6 7 3 8 4 2 2
8 6 5 5 6 4 6 0 9 5 4 2 1 1 1 1
8 6 7 3 4 4 6 2 6 4 3 3 6 2 0 0
6 4 3 3 4 2 2 0 1 1 2 0 1 1 1 1
57, 156
2 2 2 2 0 4 4 0 1 3 7 5 6 6 2 2
2 2 6 6 8 12 8 4 3 9 9 3 2 2 2 2
2 2 2 2 4 8 8 4 3 9 13 7 6 6 2 2
2 2 6 6 4 8 4 0 1 3 3 1 2 2 2 2
62, 110
3 3 1 5 1 1 4 6 1 1 0 2 4 4 4 8
1 1 0 2 0 0 2 2 4 4 2 6 4 4 5 11
3 3 1 5 1 1 4 6 1 1 0 2 4 4 4 8
5 5 2 8 2 2 6 10 6 6 2 10 8 8 11 21
26
10 8 8 6 11 3 6 4 10 8 4 2 5 5 6 0
10 6 7 5 5 3 3 1 5 3 6 2 4 4 0 0
8 6 6 4 7 3 4 2 6 4 4 2 3 3 2 0
4 4 3 1 5 3 3 1 3 1 2 2 0 0 0 0
74
10 8 10 4 10 6 5 3 11 7 5 5 5 3 4 0
8 6 7 3 4 4 6 2 6 4 3 3 6 2 0 0
8 6 6 4 8 4 3 1 3 3 3 3 5 3 4 0
6 4 5 1 2 2 2 2 4 2 1 1 0 0 0 0
58
3 3 2 4 1 3 6 2 1 1 3 3 4 8 4 0
3 3 2 4 5 11 10 2 5 5 13 9 2 6 0 0
3 3 2 4 1 3 6 2 5 5 13 9 6 14 4 0
3 3 2 4 5 11 10 2 1 1 3 3 0 0 0 0
78
3 3 3 3 1 5 5 1 1 1 5 5 4 6 2 0
2 2 2 2 3 13 13 3 6 6 10 10 4 4 0 0
3 3 3 3 1 5 5 1 3 3 11 11 8 14 6 0
4 4 4 4 3 9 9 3 2 2 2 2 0 0 0 0
54, 108
5 5 5 5 8 2 2 8 8 8 2 2 4 0 6 10
5 5 5 5 2 0 0 2 2 2 0 0 6 2 4 8
5 5 5 5 8 2 2 8 2 2 0 0 0 0 2 2
5 5 5 5 2 0 0 2 8 8 2 2 10 2 8 16
43
3 3 0 6 0 0 9 3 2 4 3 3 11 9 4 4
2 2 3 5 3 3 4 2 5 11 6 6 6 0 3 3
3 3 0 6 6 6 11 5 2 4 3 3 5 3 2 2
4 4 9 11 3 3 4 2 3 9 0 0 6 0 3 3
142
3 3 2 4 2 2 5 3 0 6 3 3 11 5 6 6
0 0 3 9 3 3 6 0 9 11 4 4 4 2 3 3
3 3 2 4 4 4 11 9 0 6 3 3 9 3 0 0
6 6 5 11 3 3 6 0 3 5 2 2 4 2 3 3
7, 168
34 12 9 9 6 6 6 6 6 0 3 3 3 3 3 3
9 3 0 0 3 3 3 3 6 0 3 3 3 3 3 3
12 6 3 3 0 0 0 0 6 0 3 3 3 3 3 3
9 3 0 0 3 3 3 3 6 0 3 3 3 3 3 3
35
6 6 9 3 12 6 3 3 12 12 9 3 6 0 3 3
8 8 12 4 8 4 2 2 4 4 0 0 4 0 2 2
6 6 9 3 12 6 3 3 4 4 3 1 2 0 1 1
4 4 6 2 0 0 0 0 4 4 0 0 4 0 2 2
140
6 6 8 4 12 4 4 4 12 12 8 0 6 2 4 4
9 9 12 6 9 3 0 0 3 3 2 0 3 1 2 2
6 6 8 4 12 4 4 4 6 6 4 0 0 0 0 0
3 3 4 2 3 1 0 0 3 3 2 0 3 1 2 2
27
9 7 5 7 8 0 2 10 6 6 0 0 2 2 8 8
6 2 2 6 0 0 0 0 3 1 1 3 6 6 6 6
7 5 3 5 4 0 2 6 2 2 0 0 2 2 4 4
6 6 2 2 4 0 4 8 9 3 3 9 6 6 6 6
172
6 6 4 8 8 0 6 10 9 3 0 0 2 6 5 7
6 6 2 2 0 0 0 0 3 1 2 6 6 2 5 7
6 6 4 8 4 0 2 2 3 1 0 0 2 2 3 5
6 6 2 2 4 0 4 8 9 3 2 6 6 6 7 9
29, 184
3 3 6 0 3 9 0 0 3 3 9 9 0 0 0 0
4 4 8 0 7 15 9 9 2 2 5 3 2 4 3 3
3 3 6 0 3 9 0 0 5 5 13 9 4 8 6 6
2 2 4 0 3 7 3 3 2 2 5 3 2 4 3 3
38
15 11 12 6 15 3 3 7 14 6 0 4 5 1 6 4
9 5 3 3 0 0 3 1 7 3 0 2 5 1 3 3
11 7 6 4 5 1 3 3 0 0 0 0 5 1 0 2
9 5 3 3 0 0 3 1 7 3 0 2 5 1 3 3
44
15 11 9 9 14 0 7 7 15 5 0 0 5 5 5 5
12 6 3 3 0 0 0 0 3 3 3 3 6 0 3 3
11 7 5 5 6 0 3 3 3 1 0 0 1 1 1 1
6 4 3 3 4 0 2 2 7 3 1 1 4 2 3 3
50, 76, 28, 56
5 5 8 2 8 8 4 0 8 8 13 3 4 4 0 0
8 8 13 3 13 13 6 0 4 4 6 2 0 0 0 0
5 5 8 2 8 8 4 0 8 8 13 3 4 4 0 0
2 2 3 1 3 3 2 0 0 0 0 0 0 0 0 0
14
10 8 7 7 6 6 12 0 5 5 5 5 15 5 0 0
4 4 4 4 4 4 8 0 16 8 4 4 0 0 0 0
8 6 5 5 4 4 8 0 3 3 3 3 9 3 0 0
10 6 4 4 2 2 4 0 0 0 0 0 0 0 0 0
42
10 8 4 10 5 3 16 0 6 4 4 2 15 9 0 0
7 5 4 4 5 3 4 0 12 8 8 4 0 0 0 0
8 6 4 6 5 3 8 0 6 4 4 2 5 3 0 0
7 5 4 4 5 3 4 0 0 0 0 0 0 0 0 0
23, 232
28 10 3 11 2 2 3 13 2 0 1 1 4 0 5 11
3 1 0 0 1 1 0 2 3 1 0 0 5 1 4 10
10 4 1 5 0 0 1 3 2 0 1 1 0 0 1 3
11 5 0 4 1 1 0 2 13 3 2 2 11 3 10 28
77, 178
1 1 2 0 1 3 0 0 1 5 10 4 1 3 0 0
2 2 13 3 10 28 11 3 0 4 11 5 0 2 1 1
1 1 2 0 5 11 4 0 3 11 28 10 3 13 2 2
0 0 3 1 4 10 5 1 0 0 3 1 0 2 1 1
13
5 5 10 0 10 10 0 0 10 10 15 5 0 0 0 0
9 9 18 0 14 14 4 4 1 1 2 0 1 1 1 1
5 5 10 0 10 10 0 0 8 8 13 3 2 2 2 2
1 1 2 0 2 2 0 0 1 1 2 0 1 1 1 1
162
5 5 9 1 10 8 1 1 10 10 14 2 0 2 1 1
10 10 18 2 15 13 2 2 0 0 4 0 0 2 1 1
5 5 9 1 10 8 1 1 10 10 14 2 0 2 1 1
0 0 0 0 5 3 0 0 0 0 4 0 0 2 1 1
18, 72
56 14 10 8 8 6 10 0 8 4 7 1 9 3 0 0
10 4 5 1 7 3 2 0 10 2 2 2 0 0 0 0
14 4 4 2 4 2 2 0 6 2 3 1 3 1 0 0
8 2 1 1 1 1 2 0 0 0 0 0 0 0 0 0
33, 132
41 15 16 4 18 4 3 3 18 8 6 0 4 0 2 2
16 6 8 2 6 2 0 0 3 1 0 0 2 0 1 1
15 5 6 2 8 2 1 1 4 2 2 0 0 0 0 0
4 2 2 0 0 0 0 0 3 1 0 0 2 0 1 1
5, 160
64 16 16 4 8 8 2 2 8 2 8 2 1 1 1 1
16 0 4 0 8 8 2 2 2 0 2 0 1 1 1 1
16 4 0 0 2 2 0 0 8 2 8 2 1 1 1 1
4 0 0 0 2 2 0 0 2 0 2 0 1 1 1 1
9
34 16 20 2 22 6 2 2 23 5 4 4 2 0 1 1
18 8 6 0 4 0 2 2 3 1 0 0 2 0 1 1
16 6 8 2 6 2 0 0 3 1 0 0 2 0 1 1
4 2 2 0 0 0 0 0 3 1 0 0 2 0 1 1
130
34 16 18 4 23 3 3 3 22 6 4 0 2 2 2 2
20 8 6 2 4 0 0 0 2 0 2 0 1 1 1 1
16 6 8 2 5 1 1 1 6 2 0 0 0 0 0 0
2 2 0 0 4 0 0 0 2 0 2 0 1 1 1 1
6
46 16 17 5 15 7 6 0 14 2 4 4 6 2 0 0
14 4 1 1 3 3 6 0 10 2 2 2 0 0 0 0
16 6 5 1 1 1 2 0 4 0 2 2 6 2 0 0
8 2 1 1 1 1 2 0 0 0 0 0 0 0 0 0
40
46 16 14 8 14 4 10 0 15 1 3 1 6 6 0 0
17 5 1 1 4 2 2 0 6 2 6 2 0 0 0 0
16 6 4 2 2 0 2 0 7 1 3 1 2 2 0 0
5 1 1 1 4 2 2 0 0 0 0 0 0 0 0 0
19, 200
55 13 0 16 0 0 10 10 0 0 0 0 9 3 6 6
0 0 0 0 0 0 0 0 10 2 0 4 6 2 4 4
13 3 0 4 0 0 2 2 0 0 0 0 3 1 2 2
16 4 0 4 0 0 4 4 10 2 0 4 6 2 4 4
126
2 2 0 4 0 0 2 6 0 0 0 0 2 2 2 10
0 0 0 0 0 0 0 0 2 2 0 4 2 2 4 16
2 2 0 4 0 0 2 6 0 0 0 0 2 2 2 10
4 4 0 8 0 0 4 12 6 6 0 12 10 10 16 68
36
68 16 10 10 12 0 6 6 12 4 0 0 8 0 4 4
10 2 2 2 0 0 0 0 6 2 0 0 4 0 2 2
16 4 2 2 4 0 2 2 0 0 0 0 0 0 0 0
10 2 2 2 0 0 0 0 6 2 0 0 4 0 2 2
3, 136
68 16 10 10 12 0 6 6 12 4 0 0 8 0 4 4
10 2 2 2 0 0 0 0 6 2 0 0 4 0 2 2
16 4 2 2 4 0 2 2 0 0 0 0 0 0 0 0
10 2 2 2 0 0 0 0 6 2 0 0 4 0 2 2
11, 138
13 9 9 9 12 0 6 6 12 12 0 0 12 0 6 6
9 3 6 6 0 0 0 0 6 6 0 0 6 0 3 3
9 9 3 3 12 0 6 6 0 0 0 0 0 0 0 0
9 3 6 6 0 0 0 0 6 6 0 0 6 0 3 3
46
9 7 0 12 0 0 15 5 0 0 0 0 16 8 0 8
0 0 0 0 0 0 0 0 15 9 0 12 0 0 9 3
7 5 0 8 0 0 9 3 0 0 0 0 8 4 0 4
12 8 0 12 0 0 12 4 5 3 0 4 8 4 3 5
1, 128
149 13 7 7 8 0 4 4 8 0 0 0 4 0 2 2
7 1 0 0 0 0 0 0 4 0 0 0 2 0 1 1
13 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
7 1 0 0 0 0 0 0 4 0 0 0 2 0 1 1
10
25 15 15 9 20 0 12 0 20 12 0 0 16 0 0 0
15 5 9 3 0 0 0 0 12 4 0 0 0 0 0 0
15 9 5 3 12 0 4 0 0 0 0 0 0 0 0 0
9 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0
4, 32
114 16 18 0 15 5 0 0 15 3 6 0 0 0 0 0
18 2 4 0 6 2 0 0 0 0 0 0 0 0 0 0
16 2 2 0 3 1 0 0 5 1 2 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12, 24, 34
16 12 20 0 24 8 0 0 24 12 12 0 0 0 0 0
20 12 16 0 12 4 0 0 0 0 0 0 0 0 0 0
12 8 12 0 12 4 0 0 8 4 4 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2, 8
88 20 24 0 28 0 0 0 28 4 0 0 0 0 0 0
24 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
20 4 4 0 4 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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