Thanks for your replies. First of all, it would already be interesting to find a covering with all integers > 100. Obviously, as you point out, a computer prog

Thanks for your replies. First of all, it would already be interesting to find a covering with all integers > 100. Obviously, as you point out, a computer program cannot be expected to prove this for every N. However, it is not clear that the answer to either of my questions should be yes. It seems it should be possible (?) to come up with an impossibility proof by computer. Certainly new insights are required as you say, and nobody expects a brute force search to work. I am wondering whether the important insights might come from people with serious CS background.