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Program to check if N is a Octadecagon number
  • Last Updated : 23 Mar, 2021

Given a number N, the task is to check if N is a Octadecagon Number or not. If the number N is an Octadecagon Number then print “Yes” else print “No”.
 

Octadecagon Number is a 18-sided polygon. The first few Octadecagon Numbers are 1, 18, 51, 100, 165, 246, 343, … 
 

Examples: 
 

Input: N = 18 
Output: Yes 
Explanation: 
Second Octadecagon number is 18.
Input: N = 30 
Output: No 
 

 



Approach: 
 

  1. The Kth term of the Octadecagon number is given as
    K^{th} Term = \frac{16*K^{2} - 14*K}{2}
     
  2. As we have to check that the given number can be expressed as a Octadecagon Number or not. This can be checked as: 
     

=> N = \frac{16*K^{2} - 14*K}{2}
=> K = \frac{14 + \sqrt{128*N + 196}}{32}
 

  1.  
  2. If the value of K calculated using the above formula is an integer, then N is a Octadecagon Number.
  3. Else N is not a Octadecagon Number.

Below is the implementation of the above approach:
 

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if N is a
// Octadecagon Number
bool isOctadecagon(int N)
{
    float n
        = (14 + sqrt(128 * N + 196))
          / 32;
 
    // Condition to check if the
    // number is a Octadecagon number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 18;
 
    // Function call
    if (isOctadecagon(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java




// Java program for the above approach
import java.lang.Math;
 
class GFG{
     
// Function to check if N is a
// octadecagon Number
public static boolean isOctadecagon(int N)
{
    double n = (14 + Math.sqrt(128 * N +
                               196)) / 32;
     
    // Condition to check if the
    // number is a octadecagon number
    return (n - (int)n) == 0;
}
 
// Driver Code   
public static void main(String[] args)
{
         
    // Given Number
    int N = 18;
     
    // Function call
    if (isOctadecagon(N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by divyeshrabadiya07

Python3




# Python3 program for the above approach
import math
 
# Function to check if N is a
# octadecagon number
def isOctadecagon(N):
 
    n = (14 + math.sqrt(128 * N + 196)) // 32
     
    # Condition to check if the
    # number is a octadecagon number
    return ((n - int(n)) == 0)
 
# Driver code
if __name__=='__main__':
     
    # Given number
    N = 18
     
    # Function Call
    if isOctadecagon(N):
        print('Yes')
    else:
        print('No')
 
# This code is contributed by rutvik_56

C#




// C# program for the above approach
using System;
class GFG{
     
// Function to check if N is a
// octadecagon Number
public static bool isOctadecagon(int N)
{
    double n = (14 + Math.Sqrt(128 * N +
                               196)) / 32;
     
    // Condition to check if the
    // number is a octadecagon number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void Main(String[] args)
{
         
    // Given Number
    int N = 18;
     
    // Function call
    if (isOctadecagon(N))
    {
        Console.WriteLine("Yes");
    }
    else
    {
        Console.WriteLine("No");
    }
}
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
 
// javascript program for the above approach
 
 
/// Function to check if N is a
// Octadecagon Number
function isOctadecagon( N)
{
    let n
        = (14 + Math.sqrt(128 * N + 196))
          / 32;
 
    // Condition to check if the
    // number is a Octadecagon number
    return (n - parseInt(n)) == 0;
}
 
 
// Driver Code
 
    // Given Number
    let N = 18;
 
    // Function Call
    if (isOctadecagon(N)) {
        document.write( "Yes");
    }
    else {
        document.write( "No");
    }
 
// This code contributed by gauravrajput1
 
</script>
Output: 
Yes

 

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