In regards to the Collatz conjecture, I have been experimenting with a consecutive growing finite set made of odd numbers < 50000
My experiment was to execute the $3n +1$ and then $n/2$ until hitting the first odd number (instead of repeating $3n+1$ till reaching $1$)
from the 50,000, the following starting numbers will hit $1$ as the first odd number: $5, 21, 85, 341, 1365, 5461, 21845$. (growing by $4n+1$)
Then i checked to see what starting points will lead to each of the above points, and you can see how it looks in the following picture:
The first noticed pattern is the repeating growth by $4n+1$
The second noticed pattern is that every 3rd number has no branches (no other starting numbers that lead to it).
What is the meaning of these patterns? and are they expected to continue like this in an infinite set?