
A   taxicab number   (the definition that is being used here)   is a positive integer that can be expressed as the sum of two positive cubes in more than one way.



The first taxicab number is   1729,   which is:

 13   +   123       and also
 93   +   103.


Taxicab numbers are also known as:

   taxi numbers
   taxi-cab numbers
   taxi cab numbers
   Hardy-Ramanujan numbers


Task

 Compute and display the lowest 25 taxicab numbers (in numeric order, and in a human-readable format).
 For each of the taxicab numbers, show the number as well as it's constituent cubes.


Extra credit
 Show the 2,000th taxicab number, and a half dozen more


See also

 A001235: taxicab numbers on The On-Line Encyclopedia of Integer Sequences.
 Hardy-Ramanujan Number on MathWorld.
 taxicab number on MathWorld.
 taxicab number on Wikipedia   (includes the story on how taxi-cab numbers came to be called).


 
use std::collections::HashMap;
use itertools::Itertools;
 
fn cubes(n: u64) -> Vec<u64> {
	let mut cube_vector = Vec::new();
	for i in 1..=n {
		cube_vector.push(i.pow(3));
	}
	cube_vector
}
 
fn main() {
	let c = cubes(1201);
	let it = c.iter().combinations(2);
	let mut m = HashMap::new();
	for x in it {
		let sum = x[0] + x[1];
		m.entry(sum).or_insert(Vec::new()).push(x)
	} 
 
	let mut result = Vec::new();
 
	for (k,v) in m.iter() {
		if v.len() > 1 {
			result.push((k,v));
		}
	}
 
	result.sort();
	for f in result {
		println!("{:?}", f);
	}
}
 