This conjecture is named after German mathematician, Lothar Collatz, who first proposed the problem in 1937.

Start with any positive integer , then apply the following recursion:

Credit: mathworld.wolfram.com |

The Collatz conjecture states the following: regardless of which positive integer is chosen initially, this sequence of numbers will always eventually reach 1.

For example, starting with 10 (which is even, so divide by 2) you get the following sequence of numbers (5,16,8,4,2,1). Or starting with 7 you get (22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1). Note that upon reaching 1 you then get (4,2,1,4,2,1...) indefinitely.

^{18}

The Collatz Conjecture has fascinated mathematicians for decades. Mathematician Paul Erdos even commented on the complexity of the problem by saying "Mathematics is not yet ready for such problems."