MC: Ping-Pong Cubes

[Valentin Albillo]

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Hi, ijabbott:

(06-25-2018 09:48 PM)ijabbott Wrote:  Thanks for all that, Valentin. That's a lot of effort you put in to this problem.

You're welcome, thanks to you for your appreciation. It wasn't that much effort, really: getting the idea for an efficient algorithm was easy, then concocting an 11-line subprogram to implement it was no big deal either, and letting my POPS system run for 12 hours straight was painless to me. The real effort was to write and properly format the post I then made to this thread, that was a very big chore. And, sadly, an almost fully wasted effort at that ... 8D

Quote:Would it be possible to post the filtering algorithm you used for deciding which PPNs to cube and check, since I understand you do not cube and check every PPN? Perhaps you could add it as an appendix after your conclusions.

Yes, sure, but not here. Apart from you it seems there's not much interest in my contributions here so I'll reserve the algorithm, code and further results for a new article to be written down in the near future, as soon as I can get some place where to upload it and further make all of my previous articles and challenges freely available on line. Sylvain kindly offered to host my HP-related materials but I've been unable to successfully ftp them up to his server so far.

Quote:My gut feeling is still that there are probably an infinite number of PPCs, mostly because infinity gives you an awful lot of wiggle room, and as you mentioned, the occurrences of PPNs and APCs seem fairly independent from each other.

Yes but my second heuristic makes it likely that the number of consecutive alternating digits lags behind the total number of digits more and more or, conversely, that the number of non-alternating digits grows and grows, in which case there will never be another PPC, infinity notwithstanding. I know of many examples where infinity would seem to give room for further results but it actually doesn't.

Thanks again for your interest and best regards.

V.
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