I should use the LaTeX more often! I agree it looks much nicer.
Hrm. So I finally got around to improving some of the N2D3P9 code. I revised things as I described so that instead of computing all of the monzos it needs to check up front (which caused crashes for large max N2D3P9), it instead works directly from the prime exponent extremas, only ever dealing with a single monzo, mutating it each time to check the next logical one until it's exhausted all the possibilities described by the extremas. Which is great! It doesn't actually speed the code up at all, but it would permit calculation of more popular ratios than 307 one day. However what I was more interested in was the prospect of hardcoding once and for all the max numerators up to N2D3P9 of 3501, per your suggestions
earlier in this thread (also brought up
here). Unfortunately, while the code *can* run to completion now, it won't ever complete, at least not in approximately 5 milliion years it won't. It says it has 33664847019245570000 monzos to check, and can check about 200,000 of them a second.
Here're the extremas:
[[0,0],[0,0],[0,9],[0,6],[0,4],[0,4],[0,3],[0,3],[0,2],[0,2],[0,2],[0,2],[0,2],[0,2],[0,2],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[0,1],[
0,1],[0,1],[0,1],[0,1],[0,1],[0,1]]
Surely the problem is the long tail at the end, going up to the 54th prime, which is 251, as you described per Johnny Reinhard's HHT. There's certainly a smarter way to get this list of numerators w/ GPF sorted by N2 and by N2P. But it's just not the most pressing thing at the moment. I'm just cleaning up the last of the to-dos I'd left for myself in the code base -- the ones I'd saved to last because I was the least excited about them