Chris, we agree on everything except cases 11, 13 and 14. In those, I get a value of n that is smaller by 1.
I think the problem is in line 20 of your code. Notice that we agree except for the cases with period 1. I checked that our codes produce the same terms for cases 1 and 11.
Thanks Chris. You wrote very clearly that n was to be the 'start' of the periodic behavior, counting the initial seed as n=1, but somehow I took it to be something else. That's an interesting discovery about the final term. I tried 100,000 random seeds up to 12-digits and didn't find anything other than the two final values you mention.
I thought about possible final values because there's a constraint on the digits of terms after the initial seed. I haven't been able to think up another possible final state. Are there only two final states?
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