hops.py

#!/usr/bin/python3

results = {}
def stats(num):
    if num in results:
        return results[num]
    if num == 1:
        return 0
    if num % 2 == 0:
        hops = stats(num // 2) + 1
        results[num] = hops
        return hops
    else:
        hops = stats(num * 3 + 1) + 1
        results[num] = hops
        return hops
    
for i in range(1000000, 1, -1):
    stats(i)

mymax = max(results, key=lambda key: results[key])
print(mymax, ' has the most hops: ', results[mymax])