# Program to check if N is a Centered Octagonal Number

• Last Updated : 23 Mar, 2021

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

Centered Octagonal number represents an octagon with a dot in the centre and others dots surrounding the centre dot in the successive octagonal layer.The first few Centered Octagonal numbers are 1, 9, 25, 49, 81, 121, 169, 225, 289, 361 …

Examples:

Input: N = 9
Output: Yes
Explanation:
Second Centered Octagonal number is 9.
Input: 16
Output: No

Approach:

1. The Kth term of the Centered Octagonal number is given as 2. As we have to check that the given number can be expressed as a Centered Octagonal 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 a Centered Octagonal Number.

4. Else N is not a Centered Octagonal 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 Centered Octagonal numberbool isCenteredOctagonal(int N){    float n        = (1 + sqrt(N))          / 2;     // Condition to check if the number    // is a Centered Octagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 9;     // Function call    if (isCenteredOctagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.util.*; class GFG{ // Function to check if the number N// is a centered octagonal numberstatic boolean isCenteredOctagonal(int N){    float n = (float) ((1 + Math.sqrt(N)) / 2);     // Condition to check if the number    // is a centered octagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){         // Given Number    int N = 9;     // Function call    if (isCenteredOctagonal(N))    {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by sapnasingh4991

## Python3

 # Python3 program for the above approachimport numpy as np # Function to check if the number N# is a centered octagonal numberdef isCenteredOctagonal(N):     n = (1 + np.sqrt(N)) / 2     # Condition to check if N    # is a centered octagonal number    return (n - int(n)) == 0 # Driver CodeN = 9 # Function callif (isCenteredOctagonal(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 centered octagonal numberstatic bool isCenteredOctagonal(int N){    float n = (float) ((1 + Math.Sqrt(N)) / 2);     // Condition to check if the number    // is a centered octagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(string[] args){         // Given Number    int N = 9;     // Function call    if (isCenteredOctagonal(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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