Check this out! The fibonacci sequence;
#, Full Value, Decimal Parity Value
1 1 1
2 1 1
3 2 2
4 3 3
5 5 5
6 8 8
7 13 4
8 21 3
9 34 7
10 55 1
11 89 8
12 144 9
13 233 8
14 377 8
15 610 7
16 987 6
17 1597 4
18 2584 1
19 4181 5
20 6765 6
21 10946 2
22 17711 8
23 28657 1
24 46368 9
25 75025 1
26 121393 1
27 196418 2
28 317811 3
29 514229 5
30 832040 8
31 1346269 4
32 2178309 3
33 3524578 7
34 5702887 1
35 9227465 8
36 14930352 9
37 24157817 8
38 39088169 8
39 63245986 7
40 102334155 6
41 165580141 4
42 267914296 1
43 433494437 5
44 701408733 6
45 1134903170 2
46 1836311903 8
47 2971215073 1
48 4807526976 9
It repeats fully in lots of 24 or half in 12!
It's more obvious if I re-number the positions by 12's. (btw, 12 is a second generation 3)
Just match the positions and observe the symmetry around 9 once more...
1 1 1
2 1 1
3 2 2
4 3 3
5 5 5
6 8 8
7 13 4
8 21 3
9 34 7
10 55 1
11 89 8
12 144 9
1 233 8
2 377 8
3 610 7
4 987 6
5 1597 5
6 2584 1
7 4181 5
8 6765 6
9 10946 2
10 17711 8
11 28657 1
12 46368 9
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
1 75025 1
2 121393 1
3 196418 2
4 317811 3
5 514229 5
6 832040 8
7 1346269 4
8 2178309 3
9 3524578 7
10 5702887 1
11 9227465 8
12 14930352 9
1 24157817 8
2 39088169 8
3 63245986 7
4 102334155 6
5 165580141 4
6 267914296 1
7 433494437 5
8 701408733 6
9 1134903170 2
10 1836311903 8
11 2971215073 1
12 4807526976 9
It's hard to display in this forum setting but hopefully you can see what I am doing here.
The decimal parity reveals the harmonics and the harmonics repeat every 24 positions.
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