2. More generally, if we define the hyper power na by
1a:=a, n+1a:=a(na) for n>=1
does the series of the last digits of 1a, 2a, 3a,... always become periodic at some point?
If so, can you provide a sharp upper limit for the period length?
Note: The hyper power na is also often denoted as a^^n.
For the first part.....
