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Program to check if N is a Icosidigonal Number
• Last Updated : 23 Mar, 2021

Given an integer N, the task is to check if it is a Icosidigonal Number or not. If the number N is an Icosidigonal Number then print “Yes” else print “No”.

Icosidigonal number
The polygon has many gons, depends on their gonal number series. In mathematics, there are a number of gonal numbers and the Icosidigonal Number is one of them and these numbers have 22 -sided polygon(icosidigon). An Icosidigonal Number belong to the class of figurative number. They have one common dots points and other dots pattern is arranged in an n-th nested Icosidigon pattern.
The first few Icosidigonal numbers are 1, 22, 63, 124, 205, 306…

Examples:

Input: N = 22
Output: Yes
Explanation:
Second Icosidigonal number is 22.
Input: 30
Output: No

Approach:

1. The Kth term of the Icosidigonal number is given as 2. As we have to check that the given number can be expressed as an Icosidigonal Number or not. This can be checked as follows –

=> => 3. If the value of K calculated using the above formula is an integer, then N is an Icosidigonal Number.

4. Else N is not an Icosidigonal 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 Icosidigonal numberbool isIcosidigonal(int N){    float n        = (18 + sqrt(160 * N + 324))          / 40;     // Condition to check if the    // number is a Icosidigonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 22;     // Function call    if (isIcosidigonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachclass GFG{ // Function to check if the number N// is a icosidigonal numberstatic boolean isIcosidigonal(int N){    float n = (float) ((18 + Math.sqrt(160 * N +                                       324)) / 40);     // Condition to check if the number    // is a icosidigonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){         // Given number    int N = 22;     // Function call    if (isIcosidigonal(N))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by Amit Katiyar

## Python3

 # Python3 program for the above approachimport numpy as np # Function to check if the number N# is a icosidigonal numberdef isIcosidigonal(N):     n = (18 + np.sqrt(160 * N + 324)) / 40     # Condition to check if N    # is a icosidigonal number    return (n - int(n)) == 0 # Driver CodeN = 22 # Function callif (isIcosidigonal(N)):    print ("Yes")else:    print ("No") # This code is contributed by PratikBasu

## C#

 // C# program for the above approachusing System; class GFG{ // Function to check if the number N// is a icosidigonal numberstatic bool isIcosidigonal(int N){    float n = (float) ((18 + Math.Sqrt(160 * N +                                    324)) / 40);     // Condition to check if the number    // is a icosidigonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(string[] args){         // Given number    int N = 22;     // Function call    if (isIcosidigonal(N))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by rutvik_56

## Javascript

 
Output:
Yes

Time Complexity: O(1)

Auxiliary Space: O(1)

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