And you can also note that all of these are Fibonacci series mod 10.
That is, each item is the sum of the previous two items mod 10. In fact, Fibonacci is often defined as starting with 1, 1, ..., but you can start with other pairs.
The (typical) 1, 1, 2, 3, 5, 8, (1)3, (2)1, (3)4, ... pattern is in the Period 60 cycle.
re(4): Solution (further analysis)
