Some interesting patterns in excellent numbers

I’ve noticed some curious patterns in excellent numbers. This relates to the Perl stuff I wrote about earlier, but this post isn’t about the Perl.

Ignoring the spaces which I use to show the pattern, each of these numbers are excellent. The pattern pivots on a 4 which can have zero or more 3s on the left side and the same number of 6s on the right side. End it all with an 8. The right half is twice the left half. I conjecture that every series of excellent numbers of a particular length has such a number. I’ll figure out the proof later: Continue reading “Some interesting patterns in excellent numbers”

Doing less work to compute excellent numbers

When I last looked at excellent numbers, I knew there was more work I could do to optimize what I was doing. In particular, I knew there was some upper limit to the range of numbers I had to check. I didn’t take the time to think about until today. I had a brief foray into other languages, such as my attempt with Julia, as I ran out of time to think about it. Continue reading “Doing less work to compute excellent numbers”

Computing excellent numbers

In the “Benchmarking” chapter of Mastering Perl, I emphasize better algorithms over different syntax. Many of the problems we think we have better solutions if we change how we do things instead of worrying about the efficiency of a particular keyword. In this item, I’ll go through my actual path through a problem rather than hiding all my failed experiments. The negative results are just as valuable. Continue reading “Computing excellent numbers”