I thought I'd might be interesting to do some "automated algorithm/turing-automata finding" (I had the busy beaver in mind). I thought about trying many in a specific language (brainfuck or smallfuck) in order to find a programm with an output as large as possible for a given input. Creating a smallfuck-programm form a integer is of course a trivial problem if the program itself does not need to be valid (unfinished loops) with conversion to base-n.
But given the condition that all n had to point to an actual program and vice verse, that different Ns point to different algorithms, and that all algorithms possible will be projected (sorry for my bad english, I don't know many CS terms).
Is this possible? Has somebody done this yet? What keywords do I have to use to find background informations on this topic?
(I know finding an algorithm this way is a kind of stupid, but maybe an answer will improve my knowledge of automatas)