notes.txt

Tasks:
 1) README.md for the binary_paths directory


Ideas:

-- Loops --
In Collatz, a number N goes to N/2 if its even and 3N+1 if its odd.
If we ignore the parity rules, how easily can we get N back to itself with a series of /2 and/or *3+1 operations?

It appears to be a nontrivial task to find a value of N that loops back to itself, even with ignoring the parity rules. With the help of a computer it's probably easy to construct these values.

After constructing/finding values that loop back to themselves, I want to see if the binary path of the loop can be a valid binary path and also if the same path is contained within another path of some N.


-- Binary path representations --
Ideas on how to present/display the binary paths:
 1) repeat the line on the Y value of each prime factors of N
 2) repeat the line on a Y value corresponding to its prime factors
   - how can we map all possible lists of prime factors to a single number?