
COMMENTS

"Destiny" means the smallest element of the cycle that the trajectory ends up in.
All seeds except those generating the cycles listed here produce an open noncyclic family (thus without lowest element) but with a regular structure like 12334444, 55667777, 123334444, 556667777, 1233334444, 5566667777,..., and with an arbitrary startup like 1, 2, 4, 8, 16, 77, 145, 668, 1345, 6677, 13444, 55778, 133345, 666677, 1333444, 5567777, 12333445, 66666677, 133333444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, ... Notice that here we fall into the regular regime starting with 1233334444 (four threes. The sequence gives 12(two threes)4444 as a representative with index 1.  Wouter Meeussen, Jul 26 2009
