#Caching
Caching
You can increase performance by caching the result. For each number generated by the sequence, cache the number and it's length in a dict. The later, if the sequence generates a number you've already seen, you can abort the sequence and add in the remaining length.
For really long sequences this can save you a lot of time.
Note: you should be caching across all runs, so that the work you do in earlier tests can be preserved during later tests.