I am quite confident that I saw a citation from Carl Woese who stated (as far as I can remember) that it was a great pity that there were exactly 20 amino acids in the standard genetic code. The reason is that, in Woese’s words, any clever person can come up with a “truthful” theory why there are 20, since it is such a neat number.
Unfortunately, quick search in the Internet does not bring any results on whether my memory is right.
And even if Woese did not say that, there are still plenty examples of looking for some arithmetical symmetries (which could be arguably called “numerology”) in the code. Just one of many examples:
Mathematical Biology 