[seqfan] Re: Will this pattern continue for all numbers?

[rgwv at rgwv.com]

confluence

-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of David Seal
Sent: Saturday, April 18, 2020 4:29 AM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Will this pattern continue for all numbers?

As a terminology suggestion, perhaps "merging point" would be better than "meeting point"? In terms of the natural meaning of the words, "merging point" implies that the two sequences become the same from that point on, like e.g. two rivers merging, whereas "meeting point" only implies they're the same at that point, like e.g. two friends meeting.

David


> On 17 April 2020 at 21:04 Tim Peters <tim.peters at gmail.com> wrote:
> 
> 
> [Ali Sada via SeqFan <seqfan at list.seqfan.eu>]
> > We start with n and use the map k-->k+p, where p alternates between 
> > the “largest prime factor” and the “smallest prime factor”.
> >
> > We have two versions here: a)    largest, smallest, largest, etc.; and
> > b)    smallest, largest, smallest, etc.
> >
> > What is interesting is that it seems, at least for the small group 
> > of numbers I checked, that no matter what version we use, we will 
> > reach a meeting point. (I can't prove that.)
> 
> "Meeting point" needs some elaboration.  When k is a power of a prime,
> (a) and (b) meet on their first iterations.  But the results later 
> seem to skip over all initial "meetings", waiting until (a) and (b) 
> diverge before a later "meeting" counts.  For example, 2 maps to 4 
> either way, and then 4 maps to 6 either way, but neither of those seem 
> to count.
> 
> ...

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