new_contents: """
  [ref.href] https://projecteuler.net/problem=14
  
  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 GetCollatzSeq(n):
      nums = []
      while True:
          nums.append(n)
          if n <= 1:
              break
          if n & 1:
              n = 3 * n + 1
          else:
              n //= 2
      return nums
  
  UPPERBOUND = 1000000
  n = 1
  maxStart = 0
  longestSeqLen = 0
  while n < UPPERBOUND:
      seq = GetCollatzSeq(n)
      seqLen = len(seq)
      if seqLen > longestSeqLen:
          maxStart = n
          longestSeqLen = seqLen
      n += 1
  
  print "A Collatz sequence starting within range under %d at number %d produces the longest chain." % (UPPERBOUND,
                                                                                                        maxStart)
  
subject: Create problem14.py