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Program to find Cullen Number
  • Last Updated : 23 Mar, 2021

A Cullen Number is a number of the form is 2n * n + 1 where n is an integer. The first few Cullen numbers are 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609 . . . . . . 
Examples: 
 

Input : n = 4
Output :65

Input : n = 0
Output : 1

Input : n = 6
Output : 161

 

Below is implementation of formula. We use bitwise left-shift operator to find 2n, then multiply the result with n and finally returns (1 << n)*n + 1. 
 

C++




// C++ program to find Cullen number
#include <bits/stdc++.h>
using namespace std;
 
// function to find n'th cullen number
unsigned findCullen(unsigned n)
{
    return (1 << n) * n + 1;
}
 
// Driver code
int main()
{
    int n = 2;
    cout << findCullen(n);
    return 0;
}

Java




// Java program to find Cullen number
import java.io.*;
 
class GFG {
    // function to find n'th cullen number
    static int findCullen(int n)
    {
        return (1 << n) * n + 1;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int n = 2;
        System.out.println(findCullen(n));
    }
}
 
// This code is contributed by vt_m.

Python3




# Python program to
# find Cullen number
 
# Function to calculate
# Cullen number
def findCullen(n):
 
    # Formula to calculate
    # nth Cullen number
     
    return (1 << n) * n + 1
 
# Driver Code
n = 2
print(findCullen(n))
 
# This code is contributed
# by aj_36                

C#




// C# program to find Cullen number
using System;
 
class GFG {
    // function to find n'th cullen number
    static int findCullen(int n)
    {
        return (1 << n) * n + 1;
    }
 
    // Driver code
    public static void Main()
    {
        int n = 2;
        Console.WriteLine(findCullen(n));
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to
// find Cullen number
 
// function to find n'th
// cullen number
function findCullen($n)
{
    return (1 << $n) * $n + 1;
}
 
    // Driver code
    $n = 2;
    echo findCullen($n);
     
// This code is contributed by ajit
?>

Javascript




<script>
 
// JavaScript program to find Cullen number
 
// function to find n'th cullen number
    function findCullen(n)
    {
        return (1 << n) * n + 1;
    }
 
// Driver Code
    let n = 2;
    document.write(findCullen(n));
 
</script>

Output: 

9

Properties of Cullen Numbers: 
 

  1. Most of the Cullen Numbers are composite numbers.
  2. n’th Cullen number is divisible by p = 2n – 1 if p is a prime number of the form 8k – 3.

Reference: https://en.wikipedia.org/wiki/Cullen_number
This article is contributed by DANISH_RAZA. 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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