Task: Taxicab numbers
C#: using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TaxicabNumber
{
    class Program
    {
        static void Main(string[] args)
        {
            IDictionary<long, IList<Tuple<int, int>>> taxicabNumbers = GetTaxicabNumbers(2006);
            PrintTaxicabNumbers(taxicabNumbers);
            Console.ReadKey();
        }

        private static IDictionary<long, IList<Tuple<int, int>>> GetTaxicabNumbers(int length)
        {
            SortedList<long, IList<Tuple<int, int>>> sumsOfTwoCubes = new SortedList<long, IList<Tuple<int, int>>>();

            for (int i = 1; i < int.MaxValue; i++)
            {
                for (int j = 1; j < int.MaxValue; j++)
                {
                    long sum = (long)(Math.Pow((double)i, 3) + Math.Pow((double)j, 3));

                    if (!sumsOfTwoCubes.ContainsKey(sum))
                    {
                        sumsOfTwoCubes.Add(sum, new List<Tuple<int, int>>());
                    }

                    sumsOfTwoCubes[sum].Add(new Tuple<int, int>(i, j));

                    if (j >= i)
                    {
                        break;
                    }
                }

                
                if (sumsOfTwoCubes.Count(t => t.Value.Count >= 2) >= length * 1.1)
                {
                    break;
                }
            }

            IDictionary<long, IList<Tuple<int, int>>> values = (from t in sumsOfTwoCubes where t.Value.Count >= 2 select t)
                .Take(2006)
                .ToDictionary(u => u.Key, u => u.Value);

            return values;
        }

        private static void PrintTaxicabNumbers(IDictionary<long, IList<Tuple<int, int>>> values)
        {
            int i = 1;

            foreach (long taxicabNumber in values.Keys)
            {
                StringBuilder output = new StringBuilder().AppendFormat("{0,10}\t{1,4}", i, taxicabNumber);

                foreach (Tuple<int, int> numbers in values[taxicabNumber])
                {
                    output.AppendFormat("\t= {0}^3 + {1}^3", numbers.Item1, numbers.Item2);
                }

                if (i <= 25 || (i >= 2000 && i <= 2006))
                {
                    Console.WriteLine(output.ToString());
                }

                i++;
            }
        }
    }
}

Java: import java.util.PriorityQueue;
import java.util.ArrayList;
import java.util.List;
import java.util.Iterator;

class CubeSum implements Comparable<CubeSum> {
	public long x, y, value;

	public CubeSum(long x, long y) {
		this.x = x;
		this.y = y;
		this.value = x*x*x + y*y*y;
	}

	public String toString() {
		return String.format("%4d^3 + %4d^3", x, y);
	}

	public int compareTo(CubeSum that) {
		return value < that.value ? -1 : value > that.value ? 1 : 0;
	}
}

class SumIterator implements Iterator<CubeSum> {
	PriorityQueue<CubeSum> pq = new PriorityQueue<CubeSum>();
	long n = 0;

	public boolean hasNext() { return true; }
	public CubeSum next() {
		while (pq.size() == 0 || pq.peek().value >= n*n*n)
			pq.add(new CubeSum(++n, 1));

		CubeSum s = pq.remove();
		if (s.x > s.y + 1) pq.add(new CubeSum(s.x, s.y+1));

		return s;
	}
}

class TaxiIterator implements Iterator<List<CubeSum>> {
	Iterator<CubeSum> sumIterator = new SumIterator();
	CubeSum last = sumIterator.next();

	public boolean hasNext() { return true; }
	public List<CubeSum> next() {
		CubeSum s;
		List<CubeSum> train = new ArrayList<CubeSum>();

		while ((s = sumIterator.next()).value != last.value)
			last = s;

		train.add(last);

		do { train.add(s); } while ((s = sumIterator.next()).value == last.value);
		last = s;

		return train;
	}
}
	
public class Taxi {
	public static final void main(String[] args) {
		Iterator<List<CubeSum>> taxi = new TaxiIterator();

		for (int i = 1; i <= 2006; i++) {
			List<CubeSum> t = taxi.next();
			if (i > 25 && i < 2000) continue;

			System.out.printf("%4d: %10d", i, t.get(0).value);
			for (CubeSum s: t)
				System.out.print(" = " + s);
			System.out.println();
		}
	}
}