Does 16 always show up in Collatz Conjecture number leading down to 1?

Question

Just wondering if 16 always shows up in number > 16 manipulation process leading down to 1 through Collatz conjecture? or are there any exceptions?

I happen to see this link with the animation showing the path only through 16.... https://www.quantamagazine.org/mathematician-terence-tao-and-the-collatz-conjecture-20191211/?fbclid=IwAR1RG-AIGWlyb3Fjtipn1jXzXw1TP5O8QWSoKe86-FhV7JmP4GbSliOBBzg

Answer 1

Well, lets do this backwards;

The only way to get to 1 is to halve 2,

The only way to get to 2 is to halve 4,

The only way to get to 4 is to halve 8,

The only way to get to 8 is to halve 16,

But 16 can be made 2 different ways - either halve 32 or times 5 by 3 and add 1. From here all the other branches branch of, and so the answer is yes; It will always pass through 16 (unless of course you start on 1,2,4 or 8)

Answer 2

Isn't that obvious ? The only way to go down is by halving.

Answer 3

En efecto 16-8-4-2-1 son la raiz Collatz, pero hay que pensar en el arbol de Collatz a lo grande. al respecto, ¿quien ha pensado en Collatz como un arbol y en sus ramificaciones? Indeed, 16-8-4-2-1 are fixed in the Collatz root, but you have to think about the Collatz tree in a big way. In this regard, who has thought of Collatz as a tree and its ramifications?