Iteratively generating a permutation of natural numbers

Question

I have a somewhat unusual question, that may or may not have been asked before (I did not find anything though, however I might just have looked for the wrong buzzwords).

Answer 1

I think you are dealing with the rank of a permutation here. (I could be wrong). I have written a Rosetta code task on this; as well as answering other SO questions on this here and here.

Is this of any use?