Project Euler Problem 14 Solution 2 (#651)

project_euler/problem_14/sol2.py

@@ -0,0 +1,16 @@
+def collatz_sequence(n):
+  """Collatz conjecture: start with any positive integer n.Next termis obtained from the previous term as follows:
+  if the previous term is even, the next term is one half the previous term.
+  If the previous term is odd, the next term is 3 times the previous term plus 1.
+  The conjecture states the sequence will always reach 1 regaardess of starting n."""
+  sequence = [n]
+  while n != 1:
+    if n % 2 == 0:# even
+      n //= 2
+    else:
+      n = 3*n +1
+    sequence.append(n)
+  return sequence
+
+answer = max([(len(collatz_sequence(i)), i)  for i in range(1,1000000)])
+print("Longest Collatz sequence under one million is %d with length %d" % (answer[1],answer[0]))