Carol Number

2.5

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 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;
} 

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));
  }
}    


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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