# Program to check if N is a Centered Hexadecagonal Number

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

Centered Hexadecagonal Number represents a dot in the centre and other dots around it in successive Hexadecagonal(16 sided polygon) layers… The first few Centered Hexadecagonal Numbers are 1, 17, 49, 97, 161, 241 …

Examples:

Input: N = 17
Output: Yes
Explanation:
Second Centered hexadecagonal number is 17.

Input: N = 20
Output: No

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

Approach:

1. The Kth term of the Centered Hexadecagonal Number is given as 2. As we have to check that the given number can be expressed as a Centered Hexadecagonal 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 Centered Hexadecagonal Number.
4. Else the number N is not a Centered Hexadecagonal 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 Centered hexadecagonal number  bool isCenteredhexadecagonal(int N)  {      float n          = (8 + sqrt(32 * N + 32))            / 16;         // Condition to check if the N is a      // Centered hexadecagonal number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      // Given Number      int N = 17;         // Function call      if (isCenteredhexadecagonal(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 the number N  // is a centered hexadecagonal number  static boolean isCenteredhexadecagonal(int N)  {      double n = (8 + Math.sqrt(32 * N + 32)) / 16;         // Condition to check if the N is a      // centered hexadecagonal number      return (n - (int)n) == 0;  }         // Driver code   public static void main(String[] args)   {              // Given Number      int N = 17;         // Function call      if (isCenteredhexadecagonal(N))       {          System.out.println("Yes");      }      else     {          System.out.println("No");      }  }   }      // This code is contributed by coder001

## Python3

 # Python3 program for the above approach   import numpy as np     # Function to check if the number N   # is a Centered hexadecagonal number   def isCenteredhexadecagonal(N):          n = (8 + np.sqrt(32 * N + 32)) / 16        # Condition to check if the N is a       # Centered hexadecagonal number       return (n - int(n)) == 0    # Driver Code   N = 17    # Function call   if (isCenteredhexadecagonal(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 centered hexadecagonal number  static bool isCenteredhexadecagonal(int N)  {      double n = (8 + Math.Sqrt(32 * N + 32)) / 16;         // Condition to check if the N is a      // centered hexadecagonal number      return (n - (int)n) == 0;  }         // Driver code   public static void Main(string[] args)   {              // Given Number      int N = 17;         // Function call      if (isCenteredhexadecagonal(N))       {          Console.Write("Yes");      }      else     {          Console.Write("No");      }  }   }      // This code is contributed by rutvik_56

Output:

Yes


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Improved By : PratikBasu, coder001, rutvik_56

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