# [seqfan] Re: corollary to the Collatz conjecture?

jean-paul allouche jean-paul.allouche at imj-prg.fr
Sat Jul 29 07:20:00 CEST 2017

```Dear Bob

I am not sure I understand your point. Do you tak the *same* map?
(i.e., x --> x/2 if x is even and (3x+1) if x is odd).
If so, the only (conjectural) loop is  (1,4,2,1).
If not, which map are you looking at?
best
jpa

Le 28/07/17 à 17:47, Bob Selcoe a écrit :
> 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
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/

```