Program to check if N is a Pentadecagonal Number

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

Pentadecagon Number is a 15-sided polygon..The first few Pentadecagon numbers are 1, 15, 42, 82, 135, 201, …

Examples:



Input: N = 15
Output: Yes
Explanation:
Second Pentadecagon number is 15.

Input: N = 30
Output: No

Approach:

  1. The Kth term of the Pentadecagon number is given as

    K^{th} Term = \frac{13*K^{2} - 11*K}{2}

  2. As we have to check that the given number can be expressed as a Pentadecagon Number or not. This can be checked as:

    => N =  \frac{13*K^{2} - 11*K}{2}
    => K = \frac{11 + \sqrt{104*N + 121}}{26}

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

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to check if N is a
// Pentadecagon number
bool isPentadecagon(int N)
{
    float n
        = (11 + sqrt(104 * N + 121))
          / 26;
  
    // Condition to check if the
    // number is a Pentadecagon number
    return (n - (int)n) == 0;
}
  
// Driver Code
int main()
{
    // Given Number
    int N = 15;
  
    // Function call
    if (isPentadecagon(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

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Java

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// Java program for the above approach
import java.io.*; 
import java.util.*; 
  
class GFG { 
  
// Function to check if N is
// a pentadecagon number
public static boolean isPentadecagon(int N)
{
    double n = (11 + Math.sqrt(104 * N + 
                               121)) / 26;
      
    // Condition to check if the number
    // is a pentadecagon number
    return (n - (int)n) == 0;
}
  
// Driver code 
public static void main(String[] args) 
      
    // Given Number
    int N = 15;
      
    // Function call
    if (isPentadecagon(N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
  
// This code is contributed by coder001

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Python3

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# Python3 program for the above approach 
from math import sqrt
  
# Function to check if N is a 
# pentadecagon number 
def isPentadecagon(N): 
  
    n = (11 + sqrt(104 * N + 121)) / 26;
      
    # Condition to check if the
    # number is a pentadecagon number
    return (n - int(n) == 0);
  
# Driver Code 
if __name__ == "__main__"
  
    # Given number 
    N = 15
  
    # Function call 
    if (isPentadecagon(N)):
        print("Yes"); 
      
    else :
        print("No"); 
      
# This code is contributed by AnkitRai01

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C#

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// C# program for the above approach
using System;
  
class GFG { 
  
// Function to check if N is
// a pentadecagon number
public static bool isPentadecagon(int N)
{
    double n = (11 + Math.Sqrt(104 * N + 
                               121)) / 26;
      
    // Condition to check if the number
    // is a pentadecagon number
    return (n - (int)n) == 0;
}
  
// Driver code 
public static void Main(String[] args) 
      
    // Given Number
    int N = 15;
      
    // Function call
    if (isPentadecagon(N))
    {
        Console.WriteLine("Yes");
    }
    else
    {
        Console.WriteLine("No");
    }
  
// This code is contributed by Amit Katiyar

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Output:

Yes

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