[seqfan] Re: Summer sequence boot camp : adding digits to theright... and more

[Lars Blomberg]

Further investigation of this iteration sequence reveals the following.

The fate of each number between 1 and 10^6 has been determined.
28300 end with 0
850 end in one of the 15 cycles
970849 grow infinitely large in one of the 24 expanding cycles.
No number grows to infinity with "random" digits, why?

Also, the count of predecessors of each number between 1 and 10^10 shows 
that a count of 0 is by far the most common with 85%.
Only 1233 numbers have 10 predecessors.
For example: 101091199 has predecessors
1918363 2827454 3736545 4645636 5554727 6463818 7372909 82810181 91009272 
91901090.

No number has been found with more than 10 predecessors.
Can this curious circumstance be proven as a fact?

/Lars