[seqfan] Collatz-like problem with prime iterations

[Vladimir Shevelev]

 Let P(n) be the maximal prime divisor of 3*n+1. For a given n, consider iterations p_1=P(n), p_2=P(p_1),

..., p_(k+1)=P(p_(k)),... I believe that, for every n, some iterate equals 2, when we stop the process.
E.g., for n=27, we have the following primes: 41,31,47,71,107,23,7,11,17,13,5,2. To every n>=1corresponds a set of primes.
The sequence of  products of primes over these sets begins with  2, 170170, 10, 130, 2, 13394810, 24310,10,170170, etc.
Let t=t(n) be the smallest number of iterates such that P^t(n)<n (n>=3). The first numbers t(n) are t(3)=2, t(4)=3, t(5)=1, t(6)=6, t(7)=4, t(8)=1, t(9)=1, t(10)=6,...(I submitted A198724).
       Is this sequence bounded? Even if the answer is in negative, the sequence of places  of records of this sequence, most likely,  grows very fast.

Regards,
Vladimir



 Shevelev Vladimir‎