# Carol Number

A Carol number is an integer of the form 4^{n} – 2^{(n+1)} – 1. An equivalent formula is (2^{n}-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 one’s in starting then single 0 in middle and then n + 1 = 4 + 1 = 5 consecutive one’s after it.

Given a number n, the task is to find the n’th 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; ` `} ` |

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## 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) ` |

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## 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)); ` ` ` `} ` `} ` |

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## 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. ` |

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## 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 ` `?> ` |

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**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.

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