The 3x + 1 problem, also known as the
Collatz problem, the Syracuse problem, Kakutani's problem,
Hasse's algorithm,
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.
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