Program to check if N is a Icositrigonal number

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

Icositrigonal number is a class of figurate number. It has 23 – sided polygon called Icositrigon. The N-th Icositrigonal number count’s the 23 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few Icositrigonol numbers are 1, 23, 66, 130, 215, 321, 448 …

Examples:

Input: N = 23
Output: Yes
Explanation:
Second icositrigonal number is 23.

Input: N = 30
Output: No



Approach:

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

    K^{th} Term =  \frac{21*K^{2} - 19*K}{2}

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

    => N = \frac{21*K^{2} - 19*K}{2}
    => K = \frac{19 + \sqrt{168*N + 361}}{42}

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

Below is the implementation of the above approach:

C++

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// C++ implementation to check that
// a number is a icositrigonal number or not
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to check that the
// number is a icositrigonal number
bool isicositrigonal(int N)
{
    float n
        = (19 + sqrt(168 * N + 361))
          / 42;
  
    // Condition to check if the
    // number is a icositrigonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
int main()
{
    int i = 23;
  
    // Function call
    if (isicositrigonal(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 a icositrigonal number or not
import java.util.*;
class GFG{
  
// Function to check that the
// number is a icositrigonal number
static boolean isicositrigonal(int N)
{
    float n = (float)(19 + Math.sqrt(168 * N + 361)) / 42;
  
    // Condition to check if the
    // number is a icositrigonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
public static void main(String args[])
{
    int i = 23;
  
    // Function call
    if (isicositrigonal(i)) 
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
  
// This code is contributed by Akanksha_Rai

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Python3

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# Python3 implementation to check that a  
# number is a icositrigonal number or not 
import math
  
# Function to check that the number 
# is a icositrigonal number 
def isicositrigonal(N): 
  
    n = (19 + math.sqrt(168 * N + 361)) / 42
  
    # Condition to check if the number  
    # is a icositrigonal number 
    return (n - int(n)) == 0
  
# Driver Code 
i = 23
  
# Function call 
if (isicositrigonal(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 a icositrigonal number or not
using System;
class GFG{
  
// Function to check that the
// number is a icositrigonal number
static bool isicositrigonal(int N)
{
    float n = (float)(19 + Math.Sqrt(168 * N + 361)) / 42;
  
    // Condition to check if the
    // number is a icositrigonal number
    return (n - (int)n) == 0;
}
  
// Driver Code
public static void Main()
{
    int i = 23;
  
    // Function call
    if (isicositrigonal(i)) 
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
  
// This code is contributed by Nidhi_Biet

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Output:

Yes

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