
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).


taxicab(n)=my(t); for(k=sqrtnint((n-1)\2,3)+1, sqrtnint(n,3), if(ispower(n-k^3, 3), if(t, return(1), t=1))); 0;
cubes(n)=my(t); for(k=sqrtnint((n-1)\2,3)+1, sqrtnint(n,3), if(ispower(n-k^3, 3, &t), print(n" =  \t"k"^3\t+ "t"^3")))
select(taxicab, [1..402597])
apply(cubes, %);