The 3n+1 problem

Indeed. In undergrad I spent a significant chunk of my spare time for about a year working on that problem.

And it gets more interesting:

In 2007, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s,[8] proved that a natural generalization of the Collatz problem is algorithmically undecidable.[7]

From http://en.wikipedia.org/wiki/Collatz_conjecture

Not knowing much about the internals of the interpreter (other than proper tco) I would assume just your old fashioned infinite loop unless it got into bignum territory and got too large for memory.

I'm sure you could use contracts to prevent the latter and reasonably sure there's some option somewhere to set maximum recursion depth to prevent the prior.

EDIT: as opposed to boring method of just putting/checking a loop count accumulator and if not bignum? into the function body.

The function doesn't look to be tail-recursive, so my guess would be a stack overflow.

Of course, if you run it and get a stack overflow, you have no way of knowing whether the number was really a counterexample or just one that took many steps to reach 1.

In that case, I'd be much too excited about making progress in mathematics to be bothered by my toy program not working right.

Yup - there are some other names to it too.

The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers,or as wondrous numbers.

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

It is.

http://projecteuler.net/problem=14

Also: "A Modified Collatz sequence": http://projecteuler.net/problem=277

There may be others.

Open invitation: drop by the MixRank office (SoMA, SF) on Wednesday evenings for friendly Project Euler competitions.