An old format
Aug. 20th, 2009 08:54 pmGood news: I have found quite a bit of unexpected regularity in my data! Something to investigate, certainly.
Bad news: If these patterns hold up, they make it harder to prove the conjecture, not easier. (Note: Earlier version said if these patterns hold up, these numbers are useless for a≥20. But now I realize that may not be the case.) (Edit again: No, wait, crap, it is.)
However, I still have yet to go and try to actually use these numbers to prove that it works, say, for a≤19, so perhaps I should do that first. (Later addition: Yeah, they do prove that. Well, now I have my answer to "how far can I push this horrible proof": 19, assuming the patterns hold up.)
-Harry
Bad news: If these patterns hold up, they make it harder to prove the conjecture, not easier. (Note: Earlier version said if these patterns hold up, these numbers are useless for a≥20. But now I realize that may not be the case.) (Edit again: No, wait, crap, it is.)
However, I still have yet to go and try to actually use these numbers to prove that it works, say, for a≤19, so perhaps I should do that first. (Later addition: Yeah, they do prove that. Well, now I have my answer to "how far can I push this horrible proof": 19, assuming the patterns hold up.)
-Harry