# Program to check if N is a Tridecagonal Number or not

Given an integer N, the task is to check if it is a Tridecagonal number or not.

Tridecagon number is a thirteen-sided polygon. The first few Tridecagon numbers are 1, 13, 36, 70, 115, 171, …

Examples:

Input: N = 13
Output: Yes
Explanation:
Second Tridecagon number is 13.

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 Tridecagon number is given as 2. As we have to check that the given number can be expressed as a Tridecagon number or not. This can be checked as follows –

=> => 3. Finally, check the value of computed using this formulae is an integer, which means that N is a Tridecagon number.

Below is the implementation of the above approach:

## C++

 // C++ implementation to check that  // a number is a Tridecagon number or not     #include     using namespace std;     // Function to check that the  // number is a Tridecagon number  bool isTridecagon(int N)  {      float n          = (9 + sqrt(88 * N + 81))            / 22;         // Condition to check if the      // number is a Tridecagon number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      int i = 13;         // Function call      if (isTridecagon(i)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that a   // number is a tridecagon number or not  class GFG{     // Function to check that the  // number is a tridecagon number  static boolean isTridecagon(int N)  {      float n = (float) ((9 + Math.sqrt(88 * N +                                        81)) / 22);         // Condition to check if the      // number is a tridecagon number      return (n - (int)n) == 0;  }     // Driver Code  public static void main(String[] args)  {      int i = 13;         // Function call      if (isTridecagon(i))      {          System.out.print("Yes");      }      else     {          System.out.print("No");      }  }  }     // This code is contributed by 29AjayKumar

## Python3

 # Python3 implementation to check that   # a number is a tridecagon number or not   import math     # Function to check that the   # number is a tridecagon number   def isTridecagon(N):          n = (9 + math.sqrt(88 * N + 81)) / 22        # Condition to check if the       # number is a tridecagon number       return (n - int(n)) == 0    # Driver Code   i = 13    # Function call   if (isTridecagon(i)):       print("Yes")   else:       print("No")             # This code is contributed by divyamohan123

## C#

 // C# implementation to check that a   // number is a tridecagon number or not  using System;     class GFG{     // Function to check that the  // number is a tridecagon number  static bool isTridecagon(int N)  {      float n = (float)((9 + Math.Sqrt(88 * N +                                       81)) / 22);         // Condition to check if the      // number is a tridecagon number      return (n - (int)n) == 0;  }     // Driver Code  public static void Main()  {      int i = 13;         // Function call      if (isTridecagon(i))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by Code_Mech

Output:

Yes


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