# Program to check if N is a Centered nonadecagonal number

• Last Updated : 16 Jul, 2021

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

Centered nonadecagonal number represents a dot in the centre and other dots surrounding it in successive nonadecagon(19 sided polygon) layers.The first few Centered nonadecagonal numbers are 1, 20, 58, 115, 191, 286

Examples:

Input: N = 20
Output: Yes
Explanation:
20 is the Second Centered nonadecagonal number is 20.
Input: 38
Output: No
Explanation:
38 is not a Centered nonadecagonal number.

Approach: To solve the problem mentioned above we have to know that the Kth term of the Centered nonadecagonal number is given as: As we have to check that the given number can be expressed as a Centered nonadecagonal number or not. This can be checked by generalizing the formula to:

=> => Finally, check the value of computation using this formula if it is an integer, if yes then it means that N is a Centered nonadecagonal number.
Below is the implementation of the above approach:

## C++

 // C++ implementation to check that// a number is a Centered// nonadecagonal number or not #include using namespace std; // Function to check that the// number is a Centered// nonadecagonal numberbool isCenterednonadecagonal(int N){    float n = (19               + sqrt(152 * N + 209))              / 38;     // Condition to check if the    // number is a Centered    // nonadecagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    int n = 20;     // Function call    if (isCenterednonadecagonal(n)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java implementation to check that// a number is a Centered// nonadecagonal number or notclass GFG{ // Function to check that the// number is a Centered// nonadecagonal numberstatic boolean isCenterednonadecagonal(int N){    float n = (float)((19 + Math.sqrt(152 * N +                                      209)) / 38);     // Condition to check if the    // number is a Centered    // nonadecagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){    int n = 20;     // Function call    if (isCenterednonadecagonal(n))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by sapnasingh4991

## Python3

 # Python3 implementation to check that# a number is a Centered# nonadecagonal number or notimport math # Function to check that the# number is a Centered# nonadecagonal numberdef isCenterednonadecagonal(N):     n = (19 + math.sqrt(152 * N +                        209)) / 38;     # Condition to check if the    # number is a Centered    # nonadecagonal number    return (n - int(n)) == 0; # Driver Coden = 20; # Function callif (isCenterednonadecagonal(n)):    print("Yes"); else:    print("No"); # This code is contributed by Code_Mech

## C#

 // C# implementation to check that// a number is a Centered// nonadecagonal number or notusing System;class GFG{ // Function to check that the// number is a Centered// nonadecagonal numberstatic bool isCenterednonadecagonal(int N){    float n = (float)((19 + Math.Sqrt(152 * N +                                      209)) / 38);     // Condition to check if the    // number is a Centered    // nonadecagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(){    int n = 20;     // Function call    if (isCenterednonadecagonal(n))    {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by Nidhi_biet

## Javascript

 

Output:

Yes

Time Complexity: O(1)
Auxiliary Space: O(1)

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