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# Carol Number

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```
Recommended Practice

## C++

 `// C++ program to find n'th Carol number``#include ``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;``}`

## Python3

 `# 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

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## Javascript

 ``

Output :

`223`

Time complexity: O(log n) , for pow function

Auxiliary Space: O(1)

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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.