65537-gon编号

给定数字N ，任务是找到^第N^个65537-gon数。

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, … 
 

例子：

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

方法：第N个65537-gon数由以下公式给出：

• 侧多边形的第N个项= $\frac{((s-2)n^2 - (s-4)n)}{2}$
• 因此65537边多边形的第N个项是

$Tn =\frac{((65537-2)n^2 - (65537-4)n)}{2} =\frac{(65535^2 - 65533)}{2}$

下面是上述方法的实现：

C++

// C++ implementation for
// above approach
#include 
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

 
// 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
 

输出：

196608

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