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@benleis@mathstodon.xyzI've been a bit negligent posting fun problems lately partly because I feel less connected to the community after leaving twitter more fully
A function maps positive integers to positive integers and it is given that
f(f(x)) = 3x
f(x+1) > f(x)
What is f(13)?
[Matt Kelly]
@benleis is the function well defined for all positive integers? But for 13 I get 22…
@apsmith I believe so
@benleis What is f(2024)?
@massimolauria @benleis That's not what I had computed, but I may have made a mistake.
@antoinechambertloir @benleis Actually I did!
@antoinechambertloir @benleis It turns out I got the method but I am not able to carry it out... :D
@massimolauria @benleis Some patience and effort will bring their fruits!
@benleis 13*sqrt(3) ?
@masp This is an positive integer to positive integer map so you'll never get something so complicated :)
@benleis I’m at a loss then :)
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@benleis a nice puzzle, thanks for posting it!
I admittedly only did the easy part of the puzzle; enumerating some of maps
@benleis Thank you! This was an enjoyable diversion while proctoring an exam yesterday. I deduced what f(13) would have to be then got quite interested in whether there was in fact any function f satisfying the hypotheses.
@benleis why not 13 * \sqrt 3 ?
@joelneely it's a positive integer to integer mapping by definition
@benleis Thanks! I missed that; too many years of FORTRAN conventions I guess. 