[seqfan] Re: Conway's subprime Fibonacci sequences

[Hans Havermann]

Wouter Meeussen:

> I submit the cycle lengths (1), 10, 11, 18, 19, 56, 136 as  
> 'potentially finite'...

Tanya Khovanova:

> We do not have a proof that these are the only cycle lengths, there  
> could be cycle lengths in between. Also, we do not have a proof that  
> there couldn't be two cycles of the same length.

A way around this might be to submit the smallest n such that the pair  
{1, n} evolves into a distinct non-trivial cycle. For example, n = {1,  
4, 36, 62, 6946, 27857, ...} evolving into the cycles of length {18,  
136, 56, 19, 11, 10, ...}. (Unfortunately, if there are other cycles,  
there is no proof that there exists an n such that {1, n} necessarily  
evolves into it.)