[seqfan] Re: Concatenate distances from n to prevprime and nextprime

[Eric Angelini]

Thank you Jack and Franklin,
Best,
É.
(sorry for the "size-zero" loop)
 

-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] De la part de Jack Brennen
Envoyé : lundi 11 janvier 2010 18:14
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Concatenate distances from n to prevprime and nextprime

Eric Angelini wrote:
> 
> I've looked for a 3rd loop -- but couldn't find any, in the
> range n=1 to 1000. Is there a possible 3rd loop somewhere?
> 

I'd conjecture there is no 3rd loop.  In fact, I'd conjecture
that there are only 73 numbers >= 3 which do not iterate to a
smaller number, and that the largest of these is 2503, which
iterates to 2618.  Any loop must necessarily contain a number
which does not iterate to a smaller number, and all of the 73
numbers end up in one of the two loops you already described.




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