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

    K^{th} Term = 8*K^{2} - 8*K + 1

  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:

    => N = 8*K^{2} - 8*K + 1
    => K = \frac{8 + \sqrt{32*N + 32}}{16}

  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++

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// C++ program for the above approach
  
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

Yes

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Improved By : PratikBasu, coder001, rutvik_56

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