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Is it possible to find a closed-form $a_n$ for some positive integers and use another formula to find the number of steps for all of those integers? If so, can you find multiple closed forms? For example, let us say you have $a_n=2^{n}$ (doesn't have to actually be this) and have another equation/s that could generate all the steps for each positive integer of that form. Is this possible?

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    This is an open problem in mathematics. The answer is not yet known to be true or false. – SlipEternal Dec 24 '19 at 19:32
  • https://math.stackexchange.com/questions/2716155/are-there-specific-numbers-for-which-the-collatz-conjecture-is-proven/2716668#2716668 – Collag3n Dec 25 '19 at 22:17
  • Even if someone could prove the collatz conjecture , considering the dynamic of the sequence , it would be a miracle if we could find a general closed form. We can only try to find a formula for as many classes of numbers as possible. – Peter Jul 24 '20 at 11:17

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