# Program to check if N is a Heptagonal Number

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

Heptagonal Number represents Heptagon and belongs to a figurative number. Heptagonal has seven angles, seven vertices, and seven-sided polygon. The first few Heptagonal Numbers are 1, 7, 18, 34, 55, 81, …

Examples:

Input: N = 7
Output: Yes
Explanation:
Second heptagonal number is 7.

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 heptagonal number is given as

2. As we have to check that the given number can be expressed as a Heptagonal 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 Heptagonal Number.
4. Else N is not a Heptagonal 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  // Heptagonal number  bool isheptagonal(int N)  {      float n          = (3 + sqrt(40 * N + 9))            / 10;         // Condition to check if the      // number is a heptagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Nuber      int N = 7;         // Function call      if (isheptagonal(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 heptagonal number  public static boolean isheptagonal(int N)  {      double n = (3 + Math.sqrt(40 * N + 9)) / 10;             // Condition to check if the number      // is a heptagonal number      return (n - (int)n) == 0;  }     // Driver code   public static void main(String[] args)   {              // Given Number      int N = 7;                 // Function call      if (isheptagonal(N))      {          System.out.println("Yes");      }      else     {          System.out.println("No");      }  }   }      // This code is contributed by coder001

## Python3

 # Python3 program for the above approach  import math     # Function to check if N is a  # heptagonal number  def isheptagonal(N):             n = (3 + math.sqrt(40 * N + 9)) / 10            # Condition to check if the      # number is a heptagonal number      return (n - int(n)) == 0        # Driver Code  N = 7    # Function call  if (isheptagonal(N)):      print("Yes")  else:      print("No")         # This code is contributed by Shubham_Coder

## C#

 // C# program for the above approach  using System;     class GFG {          // Function to check if N   // is a heptagonal number  public static bool isheptagonal(int N)  {      double n = (3 + Math.Sqrt(40 * N + 9)) / 10;             // Condition to check if the number      // is a heptagonal number      return (n - (int)n) == 0;  }     // Driver code   public static void Main(String[] args)   {              // Given Number      int N = 7;                 // Function call      if (isheptagonal(N))      {          Console.WriteLine("Yes");      }      else     {          Console.WriteLine("No");      }  }   }     // This code is contributed by Rohit_ranjan

Output:

Yes


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