Program to check if N is a Icositetragonal number

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

icositetragonal number:
s a class of figurate number. It has a 24-sided polygon called Icositetragon. The N-th Icositetragonal number count’s the number of dots and all others dots are surrounding with a common sharing corner and make a pattern
The first few icositetragonal numbers are 1, 24, 69, 136, 225, 336, …

Examples:

Input: N = 24
Output: Yes
Explanation:
Second icositetragonal number is 24.

Input: N = 30
Output: No



Approach:

  1. The Kth term of the icositetragonal number is given as

    K^{th} Term =  \frac{22*K^{2} - 20*K}{2}

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

    => N = \frac{22*K^{2} - 20*K}{2}
    => K = \frac{10 + \sqrt{44*N + 100}}{22}

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

Below is the implementation of the above approach:

C++

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// C++ implementation to check that
// a number is icositetragonal number or not
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to check that the
// number is a icositetragonal number
bool isicositetragonal(int N)
{
    float n
        = (10 + sqrt(44 * N + 100))
          / 22;
  
    // Condition to check if the
    // number is a icositetragonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
int main()
{
    int i = 24;
  
    // Function call
    if (isicositetragonal(i)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

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Java

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// Java implementation to check that
// a number is icositetragonal number or not
class GFG{
  
// Function to check that the
// number is a icositetragonal number
static boolean isicositetragonal(int N)
{
    float n = (float)((10 + Math.sqrt(44 * N + 
                                      100)) / 22);
  
    // Condition to check if the
    // number is a icositetragonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
public static void main(String[] args)
{
    int i = 24;
  
    // Function call
    if (isicositetragonal(i))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 implementation to check that 
# a number is icositetragonal number 
# or not 
import math
  
# Function to check that the number
# is a icositetragonal number 
def isicositetragonal(N): 
  
    n = (10 + math.sqrt(44 * N + 100)) / 22
  
    # Condition to check if the number 
    # is a icositetragonal number 
    return (n - int(n)) == 0
  
# Driver Code 
i = 24
  
# Function call 
if (isicositetragonal(i)): 
    print("Yes"
else
    print("No"
  
# This code is contributed by divyamohan123

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C#

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// C# implementation to check that
// a number is icositetragonal number or not
using System;
class GFG{
  
// Function to check that the
// number is a icositetragonal number
static bool isicositetragonal(int N)
{
    float n = (float)((10 + Math.Sqrt(44 * N + 
                                      100)) / 22);
  
    // Condition to check if the
    // number is a icositetragonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
public static void Main()
{
    int i = 24;
  
    // Function call
    if (isicositetragonal(i))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
  
// This code is contributed by Akanksha_Rai

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Output:

Yes

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