more as a (math-like) challange of using functional programming concepts

I see it more like a challenge too. In functional programming, there is usually a concept employed known as Y combinator. The idea is very similar like yours (including the repetition of the code), but once you define this combinator, you can use it for producing anonymous recursive functions at will. In Haskell, for instance, it is builtin and called fix (finding the fixpoint of a recursion).

http://en.wikipedia.org/wiki/Fixed_point_combinator

http://www.ece.uc.edu/~franco/C511/html/Scheme/ycomb.html

Sadly, I don't have any experience with this :-(