Taxicab Numbers

The nth Taxicab number Taxicab(n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways.
The most famous taxicab number is 1729 = Taxicab(2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).

Given a number N, print first N Taxicab(2) numbers.

Examples:

Input : N = 1
Output : 1729
Explanation : 1729 = (1 ^ 3) + (12 ^ 3) 
                   = (9 ^ 3) + (10 ^ 3)

Input : N = 2
Output : 1729 4104
Explanation : 1729 = (1 ^ 3) + (12 ^ 3) 
                   = (9 ^ 3) + (10 ^ 3)
              4104 = (16 ^ 3) + (2 ^ 3) 
                   = (15 ^ 3) + (9 ^ 3)

We try all numbers one by one and check if it is a taxicab number. To check if a number is Taxicab, we use two nested loops :
In outer loop, we calculate cube root of a number.
In inner loop, we check if there is a cube-root which yield the result.

C++

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// C++ implementation to print first N Taxicab(2) 
// numbers :
#include<bits/stdc++.h>
using namespace std;
  
void printTaxicab2(int N)
{
    // Starting from 1, check every number if
    // it is Taxicab until count reaches N.
    int i = 1, count = 0;
    while (count < N) 
    {
       int int_count = 0;
  
       // Try all possible pairs (j, k) whose cube 
       // sums can be i.
       for (int j = 1; j <= pow(i, 1.0/3); j++) 
          for (int k = j + 1; k <= pow(i, 1.0/3); k++) 
              if (j*j*j + k*k*k == i)
                  int_count++;
         
       // Taxicab(2) found
       if (int_count == 2) 
       {
          count++;
          cout << count << " " << i << endl;  
       }
  
       i++;
    }
}
  
// Driver code
int main() 
{
    int N = 5;
    printTaxicab2(N);
    return 0;
}

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Java

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// JAVA Code for Taxicab Numbers
import java.util.*;
  
class GFG {
      
    public static void printTaxicab2(int N)
    {
        // Starting from 1, check every number if
        // it is Taxicab until count reaches N.
        int i = 1, count = 0;
        while (count < N) 
        {
           int int_count = 0;
       
           // Try all possible pairs (j, k) whose  
           // cube sums can be i.
           for (int j = 1; j <= Math.pow(i, 1.0/3); j++) 
              for (int k = j + 1; k <= Math.pow(i, 1.0/3);
                                                   k++) 
                  if (j * j * j + k * k * k == i)
                      int_count++;
              
           // Taxicab(2) found
           if (int_count == 2
           {
              count++;
              System.out.println(count + " " + i);  
           }
       
           i++;
        }
    }
      
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int N = 5;
        printTaxicab2(N);
          
    }
}
    
// This code is contributed by Arnav Kr. Mandal.

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Python3

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# Python3 implementation to print
# first N Taxicab(2) numbers 
  
def printTaxicab2(N):
  
    # Starting from 1, check every number if
    # it is Taxicab until count reaches N.
    i, count = 1, 0
    while (count < N): 
      
        int_count = 0
  
        # Try all possible pairs (j, k) 
        # whose cube sums can be i.
        for j in range(1, int(pow(i, 1.0 / 3)) + 1): 
              
            for k in range(j + 1, int(pow(i, 1.0 / 3)) + 1): 
                if (j * j * j + k * k * k == i):
                    int_count += 1
          
        # Taxicab(2) found
        if (int_count == 2): 
          
            count += 1
            print(count, " ", i) 
  
        i += 1
      
# Driver code
N = 5
printTaxicab2(N)
  
# This code is contributed by Anant Agarwal.

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C#

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// C# Code for Taxicab Numbers
using System;
  
class GFG {
      
    public static void printTaxicab2(int N)
    {
        // Starting from 1, check every number if
        // it is Taxicab until count reaches N.
        int i = 1, count = 0;
        while (count < N) 
        {
            int int_count = 0;
          
            // Try all possible pairs (j, k) whose 
            // cube sums can be i.
            for (int j = 1; j <= Math.Pow(i, 1.0/3); j++) 
                for (int k = j + 1; k <= Math.Pow(i, 1.0/3);
                                                    k++) 
                    if (j * j * j + k * k * k == i)
                        int_count++;
                  
            // Taxicab(2) found
            if (int_count == 2) 
            {
                count++;
                Console.WriteLine(count + " " + i); 
            }
          
            i++;
        }
    }
      
    // Driver program 
    public static void Main() 
    {
        int N = 5;
        printTaxicab2(N);
          
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP implementation to print first
// N Taxicab(2) numbers :
  
function printTaxicab2($N)
{
      
    // Starting from 1, check every
    // number if it is Taxicab until
    // count reaches N.
    $i = 1; $count = 0;
    while ($count < $N
    {
        $int_count = 0;
      
        // Try all possible pairs (j, k)
        // whose cube sums can be i.
        for ($j = 1; $j <= pow($i, 1.0/3); $j++) 
            for ( $k = $j + 1; $k <= pow($i, 1.0/3); $k++) 
                if ($j * $j * $j + $k * $k * $k == $i)
                    $int_count++;
              
        // Taxicab(2) found
        if ($int_count == 2) 
        {
            $count++;
            echo $count, " ", $i, "\n"
        }
      
        $i++;
    }
}
  
// Driver code
  
    $N = 5;
    printTaxicab2($N);
  
// This code is contributed by ajit.
?>

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Output:

1 1729
2 4104
3 13832
4 20683
5 32832

This article is contributed by Rohit Thapliyal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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