Fine Structure

1729 Is Fine And Dandy

Curious numbers are everywhere. 1729, the first sum of two distinct numbers cubed, is the most memorable but there's no reason to choose just one arrangement. For example, do you know what the first number generated by two sums of two distinct numbers to the fourth? That would be 635318657. Or the first number by the sum of three distinct numbers cubed? 1009. Or to the fourth in that case? 6578.

In short, these taxicab numbers get to be fairly large numbers very quickly. Just for kicks I wrote up a little perl script that calculates a range of different sum-of-multiple-distinct-exponent numbers. You can configure it however you like but it's set by default for checking the familiar sums of two numbers cubed from 1 to 12 (this'll give the popular 1729).

Fork it or download it at github. It's just some quick perl using the helpful Math::Combinatorics for generating the numbers to check. I'm open to suggestions if you think you can build a better mousetrap though. Leave a comment or email me.

I'm curious to do some graphing of these numbers and see what kind of variation they produce and if you can predict some certain subset of them. This is originally why I made the script to produce a range of numbers rather than limiting it to this or that number. Perhaps I'll figure that out later.