collatz
Mathematical Programming with Python
https://people.sc.fsu.edu/~jburkardt/classes/...
python_2025/collatz/collatz.html

collatz: the Collatz conjecture suggests that a simple operation, starting at any integer and repeated indefinitely, will always end at 1. It is interesting to determine how long it takes a particular starting point to reach 1. Also, from a given starting point, the sequence of iterates can sometimes increase very high before returning to earth. We can use a Python dictionary (a new datatype we don't actually know about yet) to update a table of our results. For some related sequences, the "Mollatz", "Nollatz" and "Pollatz" sequences, it is possible to say something definite about the convergence from any starting point.

Lecture notes:

• collatz.pdf

A short article from Quanta:

• quanta_collatz.pdf

• collatz.py, given n, applies the Collatz transform, returning T(n).

• collatz_sequence.py, given n, repeatedly applies the Collatz transform until reaching 1, and prints each value as it is encountered.

• collatz_list.py, given a value of n, repeatedly applies the Collatz transform until reaching 1, and returns the entire sequence as a list.

• collatz_numpy.py, given a numpy array of one or more values of n, returns a numpy array of the Collatz transform of each value.

• collatz_dot_plot.py
• collatz_inverse.py
• collatz_len.py
• collatz_line_plot.py
• collatz_max.py
• collatz_recursion.py

• collatz_dict.py, for a given starting value n, adds each step of the Collatz sequence to a dictionary of values ( n : T(n) ).