According to a translation of the letter of Collatz to Professor Mays in 1980, Collatz mentions that he hasn't figured out whether the number n = 80 resulted in a cycle or not, concerning the collatz function. But this doesn't make sense, since the number 80 is easily computed under the collatz function. I've found the probable copy of the letter in german, but after carefully analyzing it, it isn't clear what is the number, it seems like to be 30 (which would make more sense, but still, its orbit only reaches 160 at most), or 80. My guess is that it should be 27, because this number has a really long orbit almost reaching 10000 and Collatz probably lost his patience to compute it.
The alegated copy of the letter in german can be seen in the link:
And the english translation version can be seen in:
Can someone confirm that 27 is the number, by exhibiting an explicit copy of the letter different from the one that I have? Or do you think the number is either 30 or 80?
I would appreciate any clarifying answer. Thank you.