Classification proposal based on multiples of 6
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Behavior of composite numbers

You can check more examples in the factorization tool

At each multiple of 6, every Pp present from 0 up to the observed integer changes its position in the structure for each iteration of 6.

0

+

1 = (6·0) + 1

2

3

4

6x1

5 = (6·1) - 1

6

6

7 = (6·1) + 1

8

9

10 = 5 · 2

-

11 = (6·2) - 1

12

12

+

13 = (6·2) + 1

14

15 = 5 · 3

16

-

17 = (6·3) - 1

18

18

+

19 = (6·3) + 1

20 = 5 · 4

21

22

-

23 = (6·4) - 1

24

24

+

25 = 5 · 5

26

27

28

-

29 = (6·5) - 1

30

30 = 5 · 6

+

31 = (6·5) + 1

32

33

34

-

35 = 5 · 7

36

If it is Ppₐ, the path is upwards

If it is Ppb, the path is downwards

If Pp = 6 · 1 ± 1 => At each interval it changes position
If Pp = 6 · 2 ± 1 => Every 2 intervals it changes position
...

See the case of 11, which moves upwards every two times (at 22 and 33)