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

[Neil Sloane]

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 A256970
and 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 ...