Since I personally can figure out W(n) for any n by hand given enough time, assuming I only use operations a Turing machine can do, the problem is computable, with some pattern we could find. The trick is to find a nice closed-form expression, and not an algorithm to compute it for some n given an arbitrarily large amount of time.

In short, there's probably a pattern, but like prime numbers tend to be, the pattern may well be too complex to express in ways we're used to. Then again, it may not . I'm hoping it's not, and that we can see something. Even if we just found a relation to the prime counting function, itself maddeningly complex, I'd be happy.