Program to find Cullen Number

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

Time complexity : O(1) 
Auxiliary Space : O(1)

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
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