Fun with Numbers: The Pan-Prime-Digit Cube Hypothesis

[DavidM]

(08-23-2017 12:03 AM)Claudio L. Wrote:  ...
Has anyone tried the opposite way? Look at numbers with the correct digits, discard all the ones that cannot be perfect cubes (by the sum of their digits), and simply take the cube root of the ones left?
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I had given some thought to this initially, but got hung up when thinking about how to generate all of the potential cubes that only contained the proper digits. Your idea about starting with a base 4 iteration and mapping the result to the proper digits is a nice way to achieve that. I also didn't realize until your mention of it that cubes have a characteristic "sum of digits" result (1, 8, or 9 apparently).

I'd still like to try to get something going on a 50g that will find the first known base within a reasonable (couple days?) time. I'd already been planning on a strategy involving the "only check numbers with good suffixes" approach. Perhaps I'll experiment with this one instead when I can get enough focused time to play with it!