Are there specific total stopping times that are finite for the collatz conjecture?

Question

For example, are there only certain groups of numbers that have a total stopping time of 6 or 30?

Answer 1

The conjecture is "They are all finite"

There are a lot of know "groups" of all kind, but it depends on what you look for. Do you talk about Total stopping time (reach 1) or just Stopping time (reach a smaller value) ? Are you looking at the "compressed form" (you only look at odd numbers), or the classic "shortcut form" or the "original form"?

e.g., if you want to know which numbers have a stopping time of 6 in the compressed form, here they are: $$1024k+507$$ $$1024k+347$$ $$1024k+923$$ $$1024k+583$$ $$1024k+423$$ $$1024k+999$$ $$1024k+975$$ $$1024k+815$$ $$1024k+367$$ $$1024k+735$$ $$1024k+287$$ $$1024k+575$$

If you want to know which numbers have a total stopping time of 6 in the compressed form, here is a General formula

e.g: $$19=\frac{2^{4+3+2+1+3+1}}{3^6}-\frac{2^{3+2+1+3+1}}{3^6}-\frac{2^{2+1+3+1}}{3^5}-\frac{2^{1+3+1}}{3^4}-\frac{2^{3+1}}{3^3}-\frac{2^{1}}{3^2}-\frac{2^0}{3^1} $$