[seqfan] Re: Non intersecting Fibonacci sets

Allan Wechsler acwacw at gmail.com
Sat Oct 11 19:08:32 CEST 2014

All distinct Fibonacci-like sequences eventually separate forever; this is
fairly easy to prove, since the ratio between consecutive elements
converges rapidly to phi, regardless of the starting seed. I suspect that
there is an upper limit on the number of elements two Fibonacci-like
sequences can have in common, something like 3 or 4.

On Sat, Oct 11, 2014 at 12:51 PM, Eric Angelini <Eric.Angelini at kntv.be>

> Hello SeqFans,
> I guess this is old hat, sorry;
> Let's name Fi(1,2) the Fibonacci-like
> sequence starting with 1 and 2;
> Is there a Fi(a,b) seq that has no term
> in common with Fi(1,2)?
> If yes, what is the lexico-first such seq?
> Could it be Fi(4,6)?
> If Fi(1,2) shares no term with Fi(4,6),
> is there a Fi(x,y)  seq that shares no term
> with Fi(1,2) AND Fi(4,6)?
> If yes, can we iterate that construction
> and compute more and more Fi(p,q) such seq?
> We might, in this way, arrange all integers >0
> in non intersecting Fi-sets and compute the seq S
> of the successive smallest integers belonging to each Fi-set.
> Best,
> É.
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