Create collatz_sequence.py (#639)

* Create  collatz_sequence.py

* Update and rename collatz_sequence.py to maths/collatz_sequence.py

* doctest

maths/collatz_sequence.py

@@ -0,0 +1,28 @@
+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.
+    Example:
+    >>> collatz_sequence(43)
+    [43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
+    """
+    sequence = [n]
+    while n != 1:
+        if n % 2 == 0:# even
+            n //= 2 
+        else:
+            n = 3*n +1
+        sequence.append(n)
+    return sequence
+
+
+def main():
+    n = 43
+    sequence = collatz_sequence(n)
+    print(sequence)
+    print("collatz sequence from %d took %d steps."%(n,len(sequence)))
+
+if __name__ == '__main__':
+    main()