# Program to check if N is a Centered heptagonal number

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

Centered heptagonal number is centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form..The first few Centered heptagonal number are 1, 8, 22, 43, 71, 106, 148, …

Examples:

Input: N = 8
Output: Yes
Explanation:
8 is the Second Centered heptagonal number.

Input: 20
Output: No
Explanation:
20 is not a Centered heptagonal number.

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

Approach:

To solve the problem mentioned above we have to know that the Kth term of the Centered heptagonal number is given as: As we have to check that the given number can be expressed as a Centered heptagonal number or not. This can be checked by generalizing the equation as:

=> => Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered heptagonal number.

Below is the implementation of the above approach:

## C++

 // C++ implementation to check that  // a number is a Centered  // heptagonal number or not     #include  using namespace std;     // Function to check that the  // number is a Centered  // heptagonal number  bool isCenteredheptagonal(int N)  {      float n = (7 + sqrt(56 * N - 7)) / 14;         // Condition to check if the      // number is a Centered heptagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      int n = 8;         // Function call      if (isCenteredheptagonal(n)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that   // a number is a Centered   // heptagonal number or not   import java.lang.Math;     class GFG  {         // Function to check that the   // number is a Centered   // heptagonal number   public static boolean isCenteredheptagonal(int N)   {       double n = (7 + Math.sqrt(56 * N - 7)) / 14;          // Condition to check if the       // number is a Centered heptagonal number       return (n - (int)n) == 0;   }      // Driver Code  public static void main(String[] args)   {      int n = 8;          // Function call       if (isCenteredheptagonal(n))       {           System.out.println("Yes");      }       else      {           System.out.println("No");      }   }  }     // This code is contributed by divyeshrabadiya07

## Python3

 # Python3 implementation to check   # that a number is a centered  # heptagonal number or not  import math     # Function to check that the  # number is a centered  # heptagonal number  def isCenteredheptagonal(N):             n = (7 + math.sqrt(56 * N - 7)) / 14            # Condition to check if the number      # is a centered heptagonal number      return (n - int(n)) == 0        # Driver Code  n = 8    # Function call  if (isCenteredheptagonal(n)):      print("Yes")  else:      print("No")         # This code is contributed by ShubhamCoder

## C#

 // C# implementation to check that  // a number is a centered  // heptagonal number or not  using System;     class GFG{     // Function to check that the  // number is a centered  // heptagonal number  static bool isCenteredheptagonal(int N)  {      double n = (7 + Math.Sqrt(56 * N - 7)) / 14;             // Condition to check if the number      // is a centered heptagonal number      return (n - (int)n) == 0;  }         // Driver Code  static public void Main ()  {      int n = 8;             // Function call      if (isCenteredheptagonal(n))      {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }  }     // This code is contributed by ShubhamCoder

Output:

Yes


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