# Program to check if N is a Heptadecagonal Number

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

Heptadecagonal Number is class of figurate number. It has 17-sided polygon called heptadecagon. The N-th heptadecagonal number counts the seventeen number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few heptadecagonal numbers are 1, 17, 48, 94, 155, 231…

Examples:

Input: N = 17
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 heptadecagonal number is given as 2. As we have to check that the given number can be expressed as a heptadecagonal number or not. This can be checked as follows –

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

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach  #include  using namespace std;     // Function to check if the number N  // is a heptadecagonal number  bool isheptadecagonal(int N)  {      float n          = (13 + sqrt(120 * N + 169))            / 30;         // Condition to check if number N      // is a heptadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 17;         // Function call      if (isheptadecagonal(N)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java program for the above approach  import java.util.*;     class GFG{     // Function to check if the number N  // is a heptadecagonal number  static boolean isheptadecagonal(int N)  {      float n = (float) ((13 + Math.sqrt(120 * N +                                          169)) / 30);         // Condition to check if number N      // is a heptadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void main(String[] args)  {             // Given Number      int N = 17;         // Function call      if (isheptadecagonal(N))      {          System.out.print("Yes");      }      else      {          System.out.print("No");      }  }  }     // This code is contributed by Amit Katiyar

## Python3

 # Python3 program for the above approach   import numpy as np     # Function to check if the number N   # is a heptadecagonal number   def isheptadecagonal(N):          n = (13 + np.sqrt(120 * N + 169)) / 30        # Condition to check if number N       # is a heptadecagonal number       return (n - int(n)) == 0    # Driver Code   N = 17    # Function call   if (isheptadecagonal(N)):      print("Yes")   else:      print("No")      # This code is contributed by PratikBasu

## C#

 // C# program for the above approach  using System;     class GFG{     // Function to check if the number N  // is a heptadecagonal number  static bool isheptadecagonal(int N)  {      float n = (float) ((13 + Math.Sqrt(120 * N +                                          169)) / 30);         // Condition to check if number N      // is a heptadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  public static void Main(string[] args)  {             // Given Number      int N = 17;         // Function call      if (isheptadecagonal(N))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by rutvik_56

Output:

Yes


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