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The title says it all. Are there any special class of numbers other than $2^n$ for which Collatz is true? (I mean numbers such as other powers? or some other formula that is in essence not a manipulation of $2^n$. )


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All numbers less than $20 × 2^{58} $, if that counts... – Daniel Freedman Dec 29 '11 at 12:47
Trivially, $2^nk$ for any fixed $k$ known to satisfy the conjecture. – Ilmari Karonen Dec 29 '11 at 12:53

By the work of Ştefan Andrei, Manfred Kudlek, Radu Ştefan Niculescu, there are some more infinite sets of numbers for which the conjecture holds. There was a related question on MO here.

P.S. :Currently, the server I am using requires a subscription. I hope I will explain the details at a later date. If someone has access, please help.

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