Find nth Magic Number - GeeksforGeeks

A magic number is defined as a number which can be expressed as a power of 5 or sum of unique powers of 5. First few magic numbers are 5, 25, 30(5 + 25), 125, 130(125 + 5), ….

Write a function to find the nth Magic number.

Example:

Input: n = 2
Output: 25

Input: n = 5
Output: 130

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

If we notice carefully the magic numbers can be represented as 001, 010, 011, 100, 101, 110 etc, where 001 is 0*pow(5,3) + 0*pow(5,2) + 1*pow(5,1). So basically we need to add powers of 5 for each bit set in given integer n.

Below is the implementation based on this idea.

C++

// C++ program to find nth magic numebr 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find nth magic numebr 
int nthMagicNo(int n) 
{ 
    int pow = 1, answer = 0; 
  
    // Go through every bit of n 
    while (n) 
    { 
       pow = pow*5; 
  
       // If last bit of n is set 
       if (n & 1) 
         answer += pow; 
  
       // proceed to next bit 
       n >>= 1;  // or n = n/2 
    } 
    return answer; 
} 
  
// Driver program to test above function 
int main() 
{ 
    int n = 5; 
    cout << "nth magic number is " << nthMagicNo(n) << endl; 
    return 0; 
} 

Java

// Java program to find nth 
// magic numebr 
import java.io.*; 
  
class GFG  
{ 
  // Function to find nth magic number 
  static int nthMagicNo(int n) 
  { 
     int pow = 1, answer = 0; 
   
     // Go through every bit of n 
     while (n != 0) 
     { 
       pow = pow*5; 
   
       // If last bit of n is set 
       if ((int)(n & 1) == 1) 
         answer += pow; 
   
       // proceed to next bit 
       // or n = n/2 
       n >>= 1;   
     } 
     return answer; 
  } 
   
  // Driver program to test 
  // above function 
  public static void main(String[] args) 
  { 
    int n = 5; 
    System.out.println("nth magic" + 
    " number is " + nthMagicNo(n)); 
  } 
} 
  
  
// This code is contributed by 
// prerna saini 

Python3

# Python program to find nth magic numebr 
  
# Function to find nth magic numebr 
def nthMagicNo(n): 
  
    pow = 1
    answer = 0
  
    # Go through every bit of n 
    while (n): 
  
        pow = pow*5
  
        # If last bit of n is set 
        if (n & 1): 
            answer += pow
  
        # proceed to next bit 
        n >>= 1 # or n = n/2 
      
    return answer 
  
  
# Driver program to test above function 
n = 5
print("nth magic number is", nthMagicNo(n)) 
  
# This code is contributed by 
# Smitha Dinesh Semwal 

C#

// C# program to find nth 
// magic numebr 
using System; 
  
public class GFG  
{ 
      
// Function to find nth magic number 
static int nthMagicNo(int n) 
{ 
    int pow = 1, answer = 0; 
  
    // Go through every bit of n 
    while (n != 0) 
    { 
        pow = pow * 5; 
  
        // If last bit of n is set 
        if ((int)(n & 1) == 1) 
            answer += pow; 
      
        // proceed to next bit 
        // or n = n/2 
        n >>= 1;  
    } 
    return answer; 
} 
  
// Driver Code 
public static void Main() 
{ 
    int n = 5; 
    Console.WriteLine("nth magic" +    " number is "
                       + nthMagicNo(n)); 
  
} 
} 
  
// This code is contributed by Sam007 

PHP

<?php 
// PHP program to find nth  
// magic number  
  
// Function to find nth  
// magic number 
function nthMagicNo($n) 
{ 
    $pow = 1;  
    $answer = 0; 
  
    // Go through every bit of n 
    while ($n) 
    { 
    $pow = $pow * 5; 
  
    // If last bit of n is set 
    if ($n & 1) 
        $answer += $pow; 
  
    // proceed to next bit 
    $n >>= 1; // or $n = $n/2 
    } 
    return $answer; 
} 
  
// Driver Code 
$n = 5; 
echo "nth magic number is ",  
       nthMagicNo($n), "\n"; 
  
// This code is contributed by Ajit. 
?> 

Output :

 nth magic number is 130

Thanks to manrajsingh for suggesting above solution.

This article is contributed by Abhay. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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