[digama]

You just defined a subset of the natural numbers, and asserted it has a Godel number. Sorry, there are uncountably many subsets of natural numbers and countably many Godel numbers, so there is no guarantee that this is possible. More subtly, you can consider many "natural" classes of functions, such as computable functions, recursively enumerable functions, etc. and for each such enumeration there will be a "natural" function that escapes the class. Functions to do with definability or (in this case) 'interestingness' are especially susceptible to this. See also "Tarski's theorem on the undefinability of truth".