Program to check if N is an Icosikaioctagonal Number

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

An icosikaioctagonal number is class of figurate number. It has 28 – sided polygon called icosikaioctagon. The N-th icosikaioctagonal number count’s the 28 number of dots and all other dots are surrounding with a common sharing corner and make a pattern. The first few icosikaioctagonol numbers are 1, 28, 81, 160 …

Examples:

Input: N = 28
Output: Yes
Explanation:
Second icosikaioctagonal number is 28.

Input: 30
Output: No



Approach:

  1. The Kth term of the icosikaioctagonal number is given as:

    K^{th} Term =  \frac{26*K^{2} - 24*K}{2}

  2. As we have to check that the given number can be expressed as a icosikaioctagonal number or not. This can be checked as follows –

    => N =  \frac{26*K^{2} - 24*K}{2}

    => K = \frac{24 + \sqrt{208*N + 576}}{52}

  3. Finally, check the value of computed using this formulae is an integer, which means that N is a icosikaioctagonal number.

Below is the implementation of the above approach:

C++

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// C++ program to check whether a
// number is an icosikaioctagonal 
// number or not
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to check whether a number
// is an icosikaioctagonal number or not
bool isicosikaioctagonal(int N)
{
    float n
        = (24 + sqrt(208 * N + 576))
          / 52;
  
    // Condition to check if the
    // number is an 
    // icosikaioctagonal number
    return (n - (int)n) == 0;
}
  
// Driver code
int main()
{
    int i = 28;
  
    if (isicosikaioctagonal(i)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

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Java

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// Java program to check whether a
// number is an icosikaioctagonal 
// number or not
class GFG{ 
  
// Function to check whether a
// number is an icosikaioctagonal 
// number or not
static boolean isicosikaioctagonal(int N) 
    float n = (float) ((24 + Math.sqrt(208 * N + 
                                       576)) / 52);
      
    // Condition to check whether a
    // number is an icosikaioctagonal 
    // number or not
    return (n - (int)n) == 0
  
// Driver Code 
public static void main(String[] args) 
      
    // Given number 
    int N = 28
      
    // Function call 
    if (isicosikaioctagonal(N)) 
    
        System.out.print("Yes"); 
    
    else
    
        System.out.print("No"); 
    
  
// This code is contributed by shubham

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Python3

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# Python3 program to check whether a
# number is an icosikaioctagonal 
# number or not
import math
  
# Function to check whether a number
# is an icosikaioctagonal number or not
def isicosikaioctagonal(N):
  
    n = (24 + math.sqrt(208 * N +
                        576)) // 52;
  
    # Condition to check if the
    # number is an 
    # icosikaioctagonal number
    return (n - int(n)) == 0;
  
# Driver code
i = 28;
  
if (isicosikaioctagonal(i)):
    print("Yes");
else:
    print("No");
  
# This code is contributed by Code_Mech

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C#

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// C# program to check whether a
// number is an icosikaioctagonal 
// number or not
using System;
class GFG{ 
  
// Function to check whether a
// number is an icosikaioctagonal 
// number or not
static bool isicosikaioctagonal(int N) 
    float n = (float)((24 + Math.Sqrt(208 * N + 
                                      576)) / 52);
      
    // Condition to check whether a
    // number is an icosikaioctagonal 
    // number or not
    return (n - (int)n) == 0; 
  
// Driver Code 
public static void Main() 
      
    // Given number 
    int N = 28; 
      
    // Function call 
    if (isicosikaioctagonal(N)) 
    
        Console.Write("Yes"); 
    
    else
    
        Console.Write("No"); 
    
  
// This code is contributed by Code_Mech

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Output:

Yes

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