
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).


(load "@lib/simul.l")
 
(off 'B)
(for L (subsets 2 (range 1 1200))
   (let K (sum '((N) (** N 3)) L)
      (ifn (lup B K)
         (idx 'B (list K 1 (list L)) T)
         (inc (cdr @))
         (push (cddr @) L) ) ) )
(setq R
   (filter
      '((L) (>= (cadr L) 2))
      (idx 'B)) )
(for L (head 25 R)
   (println (car L) (caddr L)) )
(for L (head 7 (nth R 2000))
   (println (car L) (caddr L)) )