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- #The following iterative sequence is defined for the set of positive integers:
- #n → n/2 (n is even)
- #n → 3n + 1 (n is odd)
- #Using the rule above and starting with 13, we generate the following sequence:
- #13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
- #It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been #proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
- #Which starting number, under one million, produces the longest chain?
- #NOTE: Once the chain starts the terms are allowed to go above one million.
- def isEven(n):
- if n%2 == 0:
- return True
- else:
- return False
- def isOdd(n):
- if n%2 == 0:
- return False
- else:
- return True
- maxChain = 0
- maxStart = 0
- for i in range(2,1000000):
- n = i
- count = 1
- while n != 1:
- if isEven(n):
- n = n/2
- count += 1
- else:
- n = (3*n) + 1
- count += 1
- if count > maxChain:
- maxChain = count
- maxStart = i
- print maxChain,maxStart
- #Improvement (Not implemented): only check odd n. it was proved empirically that the chain length of odd starting numbers was always equal to or larger than the previous even starting number.
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