From: Periodic characteristics of the Josephus ring and its application in image scrambling
j | Original sequence (A n ) | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
1 | 3 | 6 | 9 | 12 | 15 | 18 | 1 | 5 | 10 | 14 | 19 | 4 | 11 | 17 | 7 | 16 | 8 | 2 | 13 | 20 |
2 | 9 | 18 | 10 | 4 | 7 | 2 | 3 | 15 | 14 | 17 | 13 | 12 | 19 | 8 | 1 | 16 | 5 | 6 | 11 | 20 |
3 | 10 | 2 | 14 | 12 | 1 | 6 | 9 | 7 | 17 | 8 | 11 | 4 | 13 | 5 | 3 | 16 | 15 | 18 | 19 | 20 |
4 | 14 | 6 | 17 | 4 | 3 | 18 | 10 | 1 | 8 | 5 | 19 | 12 | 11 | 15 | 9 | 16 | 7 | 2 | 13 | 20 |
5 | 17 | 18 | 8 | 12 | 9 | 2 | 14 | 3 | 5 | 15 | 13 | 4 | 19 | 7 | 10 | 16 | 1 | 6 | 11 | 20 |
6 | 8 | 2 | 5 | 4 | 10 | 6 | 17 | 9 | 15 | 7 | 11 | 12 | 13 | 1 | 14 | 16 | 3 | 18 | 19 | 20 |
7 | 5 | 6 | 15 | 12 | 14 | 18 | 8 | 10 | 7 | 1 | 19 | 4 | 11 | 3 | 17 | 16 | 9 | 2 | 13 | 20 |
8 | 15 | 18 | 7 | 4 | 17 | 2 | 5 | 14 | 1 | 3 | 13 | 12 | 19 | 9 | 8 | 16 | 10 | 6 | 11 | 20 |
9 | 7 | 2 | 1 | 12 | 8 | 6 | 15 | 17 | 3 | 9 | 11 | 4 | 13 | 10 | 5 | 16 | 14 | 18 | 19 | 20 |
10 | 1 | 6 | 3 | 4 | 5 | 18 | 7 | 8 | 9 | 10 | 19 | 12 | 11 | 14 | 15 | 16 | 17 | 2 | 13 | 20 |
30 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |