[seqfan] Re: corollary to the Collatz conjecture?

[Jack Brennen]

I believe this is just equivalent to the Collatz conjecture itself.

The trajectory of any such sequence will eventually end up constrained 
to only those integers which are divisible by 3 exactly k times, and
at that point, the sequence will basically act like the base Collatz
sequence scaled up by 3^k.


- Jack


On 7/28/2017 8:47 AM, Bob Selcoe wrote:
> 
> Hi Seqfans,
> 
> I'm wondering if there is a corollary to the Collatz conjecture for k >= 0, that 3x + 3^k eventually terminate with a 4-term loop [3^k => 4*3^k => 2*3^k => 3^k].
> 
> So 3x+1 is simply k=0 with terminal loop [1,4,2,1];  k=1 is 3x+3 with loop [3,12,6,3];  k=2 is 3x+9 with loop [9,36,18,9]; etc.
>   
> There do not appear to be any OEIS entries pertaining to k > 0.
> 
>   I don't know how to program so I can't systematically test the conjecture, but doing some sequences by hand using this online tool http://www.dcode.fr/collatz-conjecture suggests it may hold.
> 
> Does anyone know if this has been tested, or if there are any papers specifically addressing the question?
> 
> Cheers,
> Bob Selcoe
> 
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