[seqfan] Collatz trajectories of 9^15-1 and 9^16-1 converge rapidly

[David Rabahy]

So far I haven't found other examples of rapid convergence like this;

9^15-1              9^16-1
205,891,132,094,648 1,853,020,188,851,840
102,945,566,047,324   926,510,094,425,920
 51,472,783,023,662   463,255,047,212,960
 25,736,391,511,831   231,627,523,606,480
 77,209,174,535,494   115,813,761,803,240
 38,604,587,267,747    57,906,880,901,620
115,813,761,803,242    28,953,440,450,810
 57,906,880,901,621    14,476,720,225,405
173,720,642,704,864    43,430,160,676,216
 86,860,321,352,432           ...
 43,430,160,676,216

9^n-1 is always divisible by 8, e.g. 9^15-1 is a multiple of 8.

9^(2^k)-1 plunges more rapidly than other equivalence classes, e.g.
9^(2^4)-1=9^16-1 is not only a multiple of 8, it has 4 more factors of 2 in
it, i.e. 9^16-1 is multiple of 2^7=128.  9^(2^k)-1 is a multiple of 2^(k+3).

9^31-1 and 9^32-1 do converge eventually but only after more than 100
Collatz trajectory steps.

Am I exploring new ground or is this all been looked at before?