Project Euler #14 - Longest Collatz Sequence in Python
Memoization

Storing results that have already been computed is known as memoization. Your current function's structure wouldn't work very well since collatzSeq isn't recursive, and you only call it with unique values. After all, the real time savers would be with all the intermediate collatz sequence values.

Restructuring your code to be recursive would make setting up the memoization a lot easier:

def collatz_seq(n):      # no space after function, snake case preferred in python
    if n == 1:           # base case
        return 1
    elif n % 2 == 0:     # recursive definitions
        return collatz_seq(n // 2) + 1     # integer division
    else:
        return collatz_seq(3*n + 1) + 1


Recusion is where you define a function in terms of itself and a base stopping condition.

Now we can easily set up memization using a dictionary:

memo = {}                               # initialize the memo dictionary
def collatz_seq(n):
    if not n in memo:                   # check if already computed
        if n == 1:                      # if not compute it
            memo[n] = 1                 # cache it
        elif n % 2 == 0:
            memo[n] = collatz_seq(n // 2) + 1
        else:
            memo[n] = collatz_seq(3*n + 1) + 1
    return memo[n]                      # and return it


So what's going on here? First we create an empty dictionary called memo. It's crated outside the function so that it persists through each function call. Next check if collatzSeq(n) has already been computed. If not compute the value, and then store it in the memo. Finally return the chached result.

This is great since once a number's collatz sequence length is computed, it never needs to be computed again. This really saves on computation time!

For more memoizaiton info check out this great SO question.

Maximum Stack Depth

Python has a maximum stack depth of 1000 (by default) which sometimes messes with recursive functions if they go too deep. I don't how long the longest collatz sequence under 1000000 is, so I don't know if this is relevent to your problem. But if you run into issues, you can change the maximum depth.