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

[DavidM]

(08-23-2017 09:15 PM)Claudio L. Wrote:  Forget my idea. Seemed as a good starting point but then I realized that:

\((n+1)^3 = n^3 + (3n^2 + 3n +1)\)...

I haven't begun my 50g version yet (other than the brief loop timing), so no lost effort there. My first "check" was going to be converting the known cube to a base 4 number (mapping 2->0, 3->1, 5->2, 7->3) and seeing how far down the list it was. Without doing the math, my guess is it would have shown up requiring too many iterations anyway. But thanks for letting me know! I'm back to my original mostly-Saturn-code plan now it seems. Even that may not be speedy enough, as I'm probably only going to be able to limit the suffix check to 6 digits due to memory constraints. I'll eventually get around to at least trying this.

(08-23-2017 09:15 PM)Claudio L. Wrote:  One thing I see is the need for a command to extract individual digits from a number, so I added a DIGITS command to newRPL, where you provide the start and end range (in powers of 10, 0=unity, 1=tens, 2=hundreds, -1=tenths, etc.) and it extracts the digits, without having to go the string route.

Cool! Even Joe's tortuous "ear worm" challenges can cause creative results in unintended ways...