I could have started with much higher seeds but 16
digit length is more than enough to display the least
chaotic sequences in 3n+1.
They all display a gradual decrease of +1 -1 digit length
difference between terms.

5065653205885988 seed and path length =206
Where the trunk branch is at 2^2^2 =16

5349460789795348 seed and path length =167
Where the trunk branch is at 2^2^4 =256

8244506962991144 seed and path length =240
Where the trunk branch is at 2^2^5 =1024

6650009958470852 seed and path length =219
Where the trunk branch is at 2^2^7 =16384

5911181468578250 seed and path length =224
Where the trunk branch is at 2^2^8 =65536

The next ones where the trunk branch is @ = 02^2^10,
2^2^11, 2^2^13, 2^2^14, 2^2^16, 2^2^17 ...
--->oo 2^2^n

Note above only 2^2^n where only certain n's make for a
possible sequence.

These least chaotic sequences can only be found with a
tree climber algorithm.

27 seed is a chaotic sequence.
As is most others.

Rulering out, of coerce,
2^2^n where n = ...10,(9.5),9,(8.5),8,(7.5),7,(6.5),6,(5.5,)5,(4.5),4,(3.5)
,3,(2.5),2
Using only certain trunk branches as above -- 16,256,1024,16384,65536...
are possible.