# 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:

Input: N = 30
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. The Kth term of the Pentadecagon number is given as 2. As we have to check that the given number can be expressed as a Pentadecagon Number or not. This can be checked as:

=> => 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++

 // C++ program for the above approach  #include  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;  }

## Java

 // 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

## Python3

 # 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

## C#

 // 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

Output:

Yes


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