65537-gon Number

Given a number N, the task is to find N^th 65537-gon number.

A 65537-gon number is a class of figurate numbers. It has a 65537-sided polygon called 65537-gon. The N-th 65537-gon number count’s the 65537 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few 65537-gon numbers are 1, 65537, 196608, 393214, 655355, 983031, …

Examples:

Input: N = 2 
Output: 65537 
Explanation:
The second 65537-gonol number is 65537. 
Input: N = 3 
Output: 196608 

Approach: The N-th 65537-gon number is given by the formula:

• Nth term of s sided polygon = 
  
• Therefore Nth term of 65537 sided polygon is
  

Below is the implementation of the above approach:

C++

// C++ implementation for
// above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the
// nth 65537-gon Number
int gonNum65537(int n)
{
    return (65535 * n * n - 65533 * n) / 2;
}

// Driver Code
int main()
{
    int n = 3;
    cout << gonNum65537(n);

    return 0;
}

Java

// Java program for above approach
class GFG{

// Function to find the
// nth 65537-gon Number
static int gonNum65537(int n)
{
    return (65535 * n * n - 65533 * n) / 2;
}

// Driver code
public static void main(String[] args)
{
    int n = 3;

    System.out.print(gonNum65537(n));
}
}

// This code is contributed by shubham

Python3

# Python3 implementation for
# above approach

# Function to find the
# nth 65537-gon Number
def gonNum65537(n):

    return (65535 * n * n - 65533 * n) // 2;

# Driver Code
n = 3;
print(gonNum65537(n));

# This code is contributed by Code_Mech

C#

// C# program for above approach
using System;
class GFG{

// Function to find the
// nth 65537-gon Number
static int gonNum65537(int n)
{
    return (65535 * n * n - 65533 * n) / 2;
}

// Driver code
public static void Main(String[] args)
{
    int n = 3;

    Console.Write(gonNum65537(n));
}
}

// This code is contributed by sapnasingh4991

Javascript

<script>

// Javascript program for above approach


    // Function to find the
    // nth 65537-gon Number
    function gonNum65537( n) {
        return (65535 * n * n - 65533 * n) / 2;
    }

    // Driver code

        let n = 3;

        document.write(gonNum65537(n));

// This code contributed by aashish1995

</script>

Output:

196608

Reference: https://en.wikipedia.org/wiki/65537-gon