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

Frank Adams-Watters franktaw at netscape.net
Sat Nov 4 11:45:16 CET 2017


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 ...

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