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:
- Most of the Cullen Numbers are composite numbers.
- 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