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.

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++ implementation of algorithm
#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 implementation of program
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 /* Driver program to run the case */
class GFG
{
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:

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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