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Carol Number
  • Difficulty Level : Medium
  • Last Updated : 22 Apr, 2021

A Carol number is an integer of the form 4n – 2(n+1) – 1. An equivalent formula is (2n-1)2 – 2.
An Interesting Property : 
For n > 2, the binary representation of the n-th Carol number is n-2 consecutive one’s, a single zero in the middle, and n + 1 more consecutive one’s. Example, n = 4 carol number is 223 and binary of 223 is 11011111, here n-2 = 4-2 = 2 consecutive ones in starting then single 0 in middle and then n + 1 = 4 + 1 = 5 consecutive ones after it.
Given a number n, the task is to find the nth Carol Number. First, few carol numbers are 1, 7, 47, 223, 959… etc.
Examples : 
 

Input : n = 2
Output: 7

Input : n = 4
Output: 223

 

 

C++




// C++ program to find n'th Carol number
#include <bits/stdc++.h>
using namespace std;
 
// Function to find n'th carol number
int carol(int n)
{
    int result = pow(2, n) - 1;
    return result * result - 2;
}
 
// Driver program to ru the case
int main()
{
    int n = 4;
    cout << carol(n);
    return 0;
}

Python




# Python program to find n'th Carol number
def carol(n):
    # a**b is a ^ b in python
    result = (2**n) - 1
    return result * result - 2
 
# driver program to run the case
n = 4
print carol(n)

Java




/* Java program to find n'th Carol number */
class GFG {
    static int carol(int n)
    {
        double tmp = Math.pow(2, n) - 1;
        return (int)tmp;
    }
 
    public static void main(String[] args)
    {
        int n = 4;
        System.out.println(carol(n));
    }
}

C#




/* C# program to find n'th Carol number */
using System;
 
class GFG {
    static int carol(int n)
    {
        int result = (int)Math.Pow(2, n) - 1;
        return result * result - 2;
    }
 
    // Driver code
    public static void Main()
    {
        int n = 4;
        Console.WriteLine(carol(n));
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to find
// n'th Carol number
 
// Function to find
// n'th carol number
function carol($n)
{
    $result = pow(2, $n) - 1;
    return $result * $result - 2;
}
 
// Driver Code
$n = 4;
echo carol($n);
 
// This code is contributed by ajit
?>

Javascript




<script>
    /* Javascript program to find n'th Carol number */
     
    function carol(n)
    {
        let result = Math.pow(2, n) - 1;
        return result * result - 2;
    }
     
    let n = 4;
      document.write(carol(n));
         
</script>

Output : 
 

223

Reference: 
https://en.wikipedia.org/wiki/Carol_number
This article is contributed by Shashank Mishra ( Gullu ). 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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

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