The Collatz conjecture states that the orbit of every number under f eventually reaches 1. And while no one has proved the conjecture, it has been verified for every number less than 268. So if you're looking for a counterexample, you can start around 300 quintillion.
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The Collatz conjecture states that the orbit of every number under f eventually reaches 1. ... Since ℊ and f are different functions, numbers have different orbits under ℊ than under f.
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