[seqfan] Re: Conway's subprime Fibonacci sequences
Hans Havermann
gladhobo at teksavvy.com
Fri Jul 27 16:44:49 CEST 2012
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.)
More information about the SeqFan
mailing list