Folding algorithm puzzle

[Josef W. Segur]

Describing the folding algorithm for pulse finding, Eric Korpela
wrote:
************************************************************
For a given array of length N, we search periods of

N/(3*2^n) to N/(4*2^n) in period steps of 1/(3*2^n) with n=0 to log_2(N/3)-1
N/(4*2^n) to N/(5*2^n) in period steps of 1/(4*2^n) with n=0 to log_2(N/4)-1
N/(5*2^n) to N/(6*2^n) in period steps of 1/(5*2^n) with n=0 to log_2(N/5)-1
************************************************************

If I've understood that correctly...

At N = 16, 20 periods are searched:
5.333.., 2.666.., 5, 2.5, 4.666.., 2.333.., 4.333.., 2.166.., 4, 2,
3.75, 1.875, 3.5, 1.75, 3.2, 1.6, 3, 1.5, 2.75, 1.375

At N = 19, 26 periods are searched:
6.333.., 3.166.., 6, 3, 5.666.., 2.833.., 5.333.., 2.166.., 5, 2.5,
4.75, 2.375, 4.5, 2.25, 4.25, 2.125, 4, 2, 3.8, 1.9, 3.6, 1.8, 3.4,
1.7, 3.2, 1.6

The puzzle is why N = 19 searching is about 7 times quicker than
N = 16 searching. There are also dips at 39, 59, 79, 99, 119, etc.
plus other variations to which I can't fit a pattern.

My measurements were made by writing the verbose output of the winnt
CLI version to a log with time tags for each line. The page at
http://freespace.virginnet.co.uk/al.braidwood/html/seti.htm
gives ample confirmation.

N Time 8K angle ranges 4K angle ranges
-- ----- ---------------- ----------------
40 48.1 0.317 thru 0.324 0.633 thru 0.648
39 15.8 0.325 thru 0.332 0.649 thru 0.664
38 32.5 0.333 thru 0.341 0.665 thru 0.682
37 46.5 0.342 thru 0.350 0.683 thru 0.701
36 54.7 0.351 thru 0.360 0.702 thru 0.721
35 38.1 0.361 thru 0.371 0.722 thru 0.742
34 37.8 0.372 thru 0.382 0.743 thru 0.764
33 56.7 0.383 thru 0.393 0.765 thru 0.787
32 53.9 0.394 thru 0.406 0.788 thru 0.812
31 16.6 0.407 thru 0.419 0.813 thru 0.839
30 15.8 0.420 thru 0.433 0.840 thru 0.867
29 17.9 0.434 thru 0.449 0.868 thru 0.898
28 28.4 0.450 thru 0.465 0.899 thru 0.930
27 17.4 0.466 thru 0.483 0.931 thru 0.966
26 17.1 0.484 thru 0.501 0.967 thru 1.003
25 28.1 0.502 thru 0.522 1.004 thru 1.044
24 17.9 0.523 thru 0.544 1.045 thru 1.089
23 17.9 0.545 thru 0.568 1.090 thru 1.137
22 19.0 0.569 thru 0.595 1.138 thru 1.190
21 32.3 0.596 thru 0.624 1.191 thru 1.248
20 33.9 0.625 thru 0.656 1.249 thru 1.312
19 5.8 0.657 thru 0.691 1.313 thru 1.383
18 23.0 0.692 thru 0.731 1.384 thru 1.462
17 38.6 0.732 thru 0.775 1.463 thru 1.551
16 41.4 0.776 thru 0.825 1.552 thru 1.651

--
Joe