Tables T(k) of numbers m*n mod k, e.g.:
T1 T2 T3 T4 T5
1 1 2 1 2 3 1 2 3 4
2 1 2 0 2 2 4 1 3
3 2 1 3 1 4 2
4 3 2 1
T6 T7 T8
1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7
2 4 0 2 4 2 4 6 1 3 5 2 4 6 0 2 4 6
3 0 3 0 3 3 6 2 5 1 4 3 6 1 4 7 2 5
4 2 0 4 2 4 1 5 2 6 3 4 0 4 0 4 0 4
5 4 3 2 1 5 3 1 6 4 2 5 2 7 4 1 6 3
6 5 4 3 2 1 6 4 2 0 6 4 2
7 6 5 4 3 2 1
T9 T10
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9
2 4 6 8 1 3 5 7 2 4 6 8 0 2 4 6 8
3 6 0 3 6 0 3 6 3 6 9 2 5 8 1 4 7
4 8 3 7 2 6 1 5 4 8 2 6 0 4 8 2 6
5 1 6 2 7 3 8 4 5 0 5 0 5 0 5 0 5
6 3 0 6 3 0 6 3 6 2 8 4 0 6 2 8 4
7 5 3 1 8 6 4 2 7 4 1 8 5 2 9 6 3
8 7 6 5 4 3 2 1 8 6 4 2 0 8 6 4 2
9 8 7 6 5 4 3 2 1
T11 T12
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11
2 4 6 8 10 1 3 5 7 9 2 4 6 8 10 0 2 4 6 8 10
3 6 9 1 4 7 10 2 5 8 3 6 9 0 3 6 9 0 3 6 9
4 8 1 5 9 2 6 10 3 7 4 8 0 4 8 0 4 8 0 4 8
5 10 4 9 3 8 2 7 1 6 5 10 3 8 1 6 11 4 9 2 7
6 1 7 2 8 3 9 4 10 5 6 0 6 0 6 0 6 0 6 0 6
7 3 10 6 2 9 5 1 8 4 7 2 9 4 11 6 1 8 3 10 5
8 5 2 10 7 4 1 9 6 3 8 4 0 8 4 0 8 4 0 8 4
9 7 5 3 1 10 8 6 4 2 9 6 3 0 9 6 3 0 9 6 3
10 9 8 7 6 5 4 3 2 1 10 8 6 4 2 0 10 8 6 4 2
11 10 9 8 7 6 5 4 3 2 1
Here we can select also (similarly as in G-systems) such numbers, which are self, not nested.
(See above - rows and columns, which do not have number 0.) Tables of self instances have φ(k) rows and columns, where φ is Euler function.
T1 T2 T3 T4 T5
1 1 2 1 3 1 2 3 4
2 1 3 1 2 4 1 3
3 1 4 2
4 3 2 1
T6 T7 T8
1 5 1 2 3 4 5 6 1 3 5 7
5 1 2 4 6 1 3 5 3 1 7 5
3 6 2 5 1 4 5 7 1 3
4 1 5 2 6 3 7 5 3 1
5 3 1 6 4 2
6 5 4 3 2 1
T9 T10
1 2 4 5 7 8 1 3 7 9
2 4 8 1 5 7 3 9 1 7
4 8 7 2 1 5 7 1 9 3
5 1 2 7 8 4 9 7 3 1
7 5 1 8 4 2
8 7 5 4 2 1
T11 T12
1 2 3 4 5 6 7 8 9 10 1 5 7 11
2 4 6 8 10 1 3 5 7 9 5 1 11 7
3 6 9 1 4 7 10 2 5 8 7 11 1 5
4 8 1 5 9 2 6 10 3 7 11 7 5 1
5 10 4 9 3 8 2 7 1 6
6 1 7 2 8 3 9 4 10 5
7 3 10 6 2 9 5 1 8 4
8 5 2 10 7 4 1 9 6 3
9 7 5 3 1 10 8 6 4 2
10 9 8 7 6 5 4 3 2 1