Python and the Collatz Conjecture

• https://en.wikipedia.org/wiki/Collatz_conjecture

Functions:

• test_num(n) # takes a positive integer and calculates the number of steps to converge to 1

• test_range(init, final) # calculates convergance for a range of positive integers

• test_range_dict(init, final) # calculates convergance for a range of positive integers using an optimized routine which utilizes previously found values in the range.

Example usages in ipython3:

%run collatz.py
test_num(1152921504606846976)   # this is 2^60
test_range(1,10000)
test_range_dict(1, 10000)

Timing

from timeit import Timer
t1 = Timer(lambda: test_range(1,100000))
t2 = Timer(lambda: test_range_dict(1,100000))
print(t1.timeit(number=1))
print(t2.timeit(number=1))