# 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.

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

## Javascript

 

Output:

Yes

Time Complexity: O(logN)

Auxiliary Space: O(1)

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