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# Program to find Cullen Number

• Last Updated : 21 Jun, 2022

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 ` `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

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## Javascript

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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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