An AI noticing any patterns in its own behaviour is not a rare case that indicates that something has already gone wrong, but, if we allow this, it will accidentally discover its own safeguards fairly quickly: they are anything that causes its behaviour to not maximize what it believes to be its utility function.
It can't discover it's safeguards, as it's eliminated if it breaks ones. These are serious, final safeguards!
You could argue that a surviving one would notice that it hadn;t happened to do various things, and would form a sort of anthropic principle that the chance of it not having to have killed a human or whatever the safeguards are are very low, to note that humans have got this safeguard system and to work out from there what they are. But I think it would be easier to work the safeguards out more directly.
At the recent London meet-up someone (I'm afraid I can't remember who) suggested that one might be able to solve the Friendly AI problem by building an AI whose concerns are limited to some small geographical area, and which doesn't give two hoots about what happens outside that area. Cipergoth pointed out that this would probably result in the AI converting the rest of the universe into a factory to make its small area more awesome. In the process, he mentioned that you can make a "fun game" out of figuring out ways in which proposed utility functions for Friendly AIs can go horribly wrong. I propose that we play.
Here's the game: reply to this post with proposed utility functions, stated as formally or, at least, as accurately as you can manage; follow-up comments explain why a super-human intelligence built with that particular utility function would do things that turn out to be hideously undesirable.
There are three reasons I suggest playing this game. In descending order of importance, they are: