Find a formula for the collatz branch numbers

Question

Context: Collatz conjecture

What I call a 'branch number', is a number accessible by 2 different routes.

Example :

• 24 is not a branch number, it can be accessed only from 48 (division by 2)
• 16 is a branch number, it can be accessed from 32 (divison by 2) or 5 (3x+1)

Is it possible to find a formula that generates these numbers or is this tied to the problem itself - so solving this would resolve the problem?

Thanks

Update

I'm talking about finding a function that generates these numbers with this sequence :

[10, 16, 22, 28, 34, 40, 46, ...]

Answer 1

[10,$\qquad$ 16,$\quad$ 22,$\qquad$ 28,$\quad$ 34,$\qquad$ 40,$\qquad$ 46, ...] can be rewritten as
[1*6+4, 2*6+4, 3*6+4, 4*6+4, 5*6+4, ...] . You surely see the pattern - and the general formula?

Answer 2

We know that odd numbers cannot be branch numbers, because they can only be generated in one way (i.e., dividing by 2). Even numbers can only be branch numbers if they are of the form $3x+1$ for some $x$. This means that all positive even numbers $e$ that satisfy $e\equiv1\mod{3}$ are branch numbers.