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# Program to check if N is a Centered Hexadecagonal Number

• Last Updated : 23 Mar, 2021

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

Centered Hexadecagonal Number represents a dot in the centre and other dots around it in successive Hexadecagonal(16 sided polygon) layers… The first few Centered Hexadecagonal Numbers are 1, 17, 49, 97, 161, 241 …

Examples:

Input: N = 17
Output: Yes
Explanation:
Second Centered hexadecagonal number is 17.
Input: N = 20
Output: No

Approach:

1. The Kth term of the Centered Hexadecagonal Number is given as

2. As we have to check that the given number can be expressed as a Centered Hexadecagonal Number or not. This can be checked as:

=>
=>

3. If the value of K calculated using the above formula is an integer, then N is a Centered Hexadecagonal Number.

4. Else the number N is not a Centered Hexadecagonal 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 hexadecagonal numberbool isCenteredhexadecagonal(int N){    float n        = (8 + sqrt(32 * N + 32))          / 16;     // Condition to check if the N is a    // Centered hexadecagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    // Given Number    int N = 17;     // Function call    if (isCenteredhexadecagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

## Java

 // Java program for the above approachimport java.io.*;import java.util.*; class GFG {     // Function to check if the number N// is a centered hexadecagonal numberstatic boolean isCenteredhexadecagonal(int N){    double n = (8 + Math.sqrt(32 * N + 32)) / 16;     // Condition to check if the N is a    // centered hexadecagonal number    return (n - (int)n) == 0;}     // Driver codepublic static void main(String[] args){         // Given Number    int N = 17;     // Function call    if (isCenteredhexadecagonal(N))    {        System.out.println("Yes");    }    else    {        System.out.println("No");    }}} // This code is contributed by coder001

## Python3

 # Python3 program for the above approachimport numpy as np # Function to check if the number N# is a Centered hexadecagonal numberdef isCenteredhexadecagonal(N):     n = (8 + np.sqrt(32 * N + 32)) / 16     # Condition to check if the N is a    # Centered hexadecagonal number    return (n - int(n)) == 0 # Driver CodeN = 17 # Function callif (isCenteredhexadecagonal(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 hexadecagonal numberstatic bool isCenteredhexadecagonal(int N){    double n = (8 + Math.Sqrt(32 * N + 32)) / 16;     // Condition to check if the N is a    // centered hexadecagonal number    return (n - (int)n) == 0;}     // Driver codepublic static void Main(string[] args){         // Given Number    int N = 17;     // Function call    if (isCenteredhexadecagonal(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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