# 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

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

## Javascript

 

Output:

Yes

Time Complexity: O(logN), for using inbuilt sqrt function.
Auxiliary Space: O(1)

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