The 3x + 1 problem, also known as the
Collatz problem, the Syracuse problem, Kakutani's problem,
and Ulam's problem,
concerns the behavior of the iterates of the function which takes odd
integers n to 3n+1 and even integers n to .
The 3x+1 Conjecture asserts that, starting from any positive integer
n, repeated iteration of this function eventually produces the value 1.