RWG, you should see work by Chowla & Selberg which I think pre-discovered what you were saying and a good deal more re factorial(n/24) for n=integer. FWL, I don't currently understand what he did, but I think he thinks he produced a fairly short inductive proof of my Knight-distance formula. (Which I'd tried, but failed, to accomplish.) So if you are right, then congratulations. Myself, I had to believe there was a proof of this general ilk, but the only ways I could see to produce it, just sort of led me into a recurrence quagmire. I couldn't un-mess the mess. So anyhow FWL's proof seems suspiciously "too easy" plus I currently am not following it. But on the other hand, it may well be I was just mentally blocked from seeing something fairly easy, while he did. Sorry to be incoherent, I'm a bit sick right now.