[seqfan] Re: Iterating "smallest odd prime divisor of n^2 + 1"

[Luca Petrone]

Dear All,

for n=4949, 6051, 9751 and 12281, at least, the map "n -> smallest odd prime divisor of n^2+1" diverges.

Regards,

Luca Petrone

> 
>     Il 4 novembre 2017 alle 11.45 Frank Adams-Watters via SeqFan <seqfan at list.seqfan.eu> ha scritto:
> 
>     It was definitely my impression that it did always fall into that loop when I looked at the question in conjunction with my edit to the related sequence A031439 back in 06. I didn't have any idea of how to prove it, however.
> 
>     Probabilistically, it seems likely: you only have to get a term congruent to 2 or 3 mod 5, and you immediately fall into the loop.
> 
>     Franklin T. Adams-Watters
> 
>     -----Original Message-----
>     From: Neil Sloane <njasloane at gmail.com>
>     To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>     Sent: Fri, Nov 3, 2017 11:59 pm
>     Subject: [seqfan] Iterating "smallest odd prime divisor of n^2 + 1"
> 
>     Dear Seq Fans, While I was at Hofstra Univ. the other day, Zoran Sunik
>     asked, if you iterate the map "n -> smallest odd prime divisor of n^2+1",
>     do you always end in the 2-cycle (5 <-> 13) ?Does anyone know?
>     See A125256 for the map, and also its bisections A256970and A293958.
>     If this is true, then there could be a sequence giving the number of
>     iterations needed to reach the loop, or to reach any loop if there are
>     others ...
> 
>     --Seqfan Mailing list - http://list.seqfan.eu/
> 
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>