# [seqfan] Re: Collatz-like problem with prime iterations

Charles Greathouse charles.greathouse at case.edu
Mon Oct 31 00:19:22 CET 2011

```Right.  In particular, Dickson's conjecture implies that the sequence
is unbounded.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Sun, Oct 30, 2011 at 1:03 AM,  <franktaw at netscape.net> wrote:
> The sequence is almost certainly unbounded. Just as there are believed to be
> arbitrarily long sequences of primes with p_(n+1) = 2*p_n + 1 (the same for
> 2*p_n - 1), there are almost certainly arbitrarily long sequences of primes
> with p_(n+1) = (3*p_n + 1) / 2.
>
>
> -----Original Message-----
> From: Vladimir Shevelev <shevelev at bgu.ac.il>
>
>  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,
>
>
>
>
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