A133117
Fractal sequence based on comparison of {n * tau} with {i*tau} for i = 1 to F(2j) where F(2j) equals the first i for which {n*tau} <= {i*tau} as i goes from 1 to F(2j+2)-1 and F(2j) equals the insertion point of n into P(n-1). The fractional parts {i*tau} are all less than or equal to {F(2j-2)*tau} for 0 < i < F(2j), so there is no chance that an insertion point greater than n in the permutation of the first n-1 integers will be specified by this rule. The table, A132827, gives the insertion points for each n into the permutation P(n-1) of the first n integers.
| n |
a(n) |
| 1 |
1 |
| 2 |
2 |
| 3 |
1 |
| 4 |
2 |
| 5 |
1 |
| 6 |
3 |
| 7 |
4 |
| 8 |
2 |
| 9 |
1 |
| 10 |
3 |
| 11 |
5 |
| 12 |
4 |
| 13 |
2 |
| 14 |
1 |
| 15 |
3 |
| 16 |
5 |
| 17 |
4 |
| 18 |
6 |
| 19 |
2 |
| 20 |
1 |
| 21 |
3 |
| 22 |
7 |
| 23 |
5 |
| 24 |
4 |
| 25 |
6 |
| 26 |
2 |
| 27 |
1 |
| 28 |
3 |
| 29 |
7 |
| 30 |
5 |
| 31 |
4 |
| 32 |
6 |
| 33 |
2 |
| 34 |
1 |
| 35 |
3 |
| 36 |
8 |
[1, 2, 1, 2, 1, 3, 4, 2, 1, 3, 5, 4, 2, 1, 3, 5, 4, 6, 2, 1, 3, 7, 5, 4, 6, 2, 1, 3, 7, 5, 4, 6, 2, 1, 3, 8]