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Mar 11 at 19:18 history became hot network question
Mar 11 at 12:20 vote accept Yaakov Baruch
Mar 11 at 12:14 comment added Yaakov Baruch @Wojowu You are right. I edited the question to reflect what I really had in mind: to assume there is an infinite orbit. I don't know if the term "stronlgy" that I used is the appropriate one though.
Mar 11 at 12:13 answer added Wojowu timeline score: 39
Mar 11 at 12:11 history edited Yaakov Baruch CC BY-SA 4.0
added 57 characters in body
Mar 11 at 11:47 comment added Wojowu How do you get $c=\infty$? It could be that all orbits settle into a cycle rather than blowing up to infinity. Anyway, Wikipedia mentions the bound that $\gg n^{0.84}$ elements below $n$ will reach $1$, and brief search suggests this is still state of the art.
Mar 11 at 11:22 history edited Yaakov Baruch CC BY-SA 4.0
edited body
Mar 11 at 11:13 history asked Yaakov Baruch CC BY-SA 4.0