# Program to check if N is a Centered Hexadecagonal Number

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 Numberrepresents a dot in the centre and other dots around it in successive Hexadecagonal(16 sided polygon) layers… The first few Centered Hexadecagonal Numbers are1, 17, 49, 97, 161, 241 …

**Examples:**

Input:N = 17Output:YesExplanation:

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

**Approach:**

1. The **K ^{th}** 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 <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if the number N` `// is a Centered hexadecagonal number` `bool` `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 Code` `int` `main()` `{` ` ` `// Given Number` ` ` `int` `N = 17;` ` ` `// Function call` ` ` `if` `(isCenteredhexadecagonal(N)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG {` ` ` `// Function to check if the number N` `// is a centered hexadecagonal number` `static` `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 code` `public` `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 approach` `import` `numpy as np` `# Function to check if the number N` `# is a Centered hexadecagonal number` `def` `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 Code` `N ` `=` `17` `# Function call` `if` `(isCenteredhexadecagonal(N)):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by PratikBasu` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG {` ` ` `// Function to check if the number N` `// is a centered hexadecagonal number` `static` `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 code` `public` `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

`<script>` `// javascript program for the above approach` `// Function to check if the number N` `// is a Centered hexadecagonal number` `function` `isCenteredhexadecagonal( N)` `{` ` ` `let n` ` ` `= (8 + Math.sqrt(32 * N + 32))` ` ` `/ 16;` ` ` `// Condition to check if the N is a` ` ` `// Centered hexadecagonal number` ` ` `return` `(n - parseInt(n)) == 0;` `}` `// Driver Code` ` ` `// Given Number` ` ` `let N = 17;` ` ` `// Function Call` ` ` `if` `(isCenteredhexadecagonal(N)) {` ` ` `document.write( ` `"Yes"` `);` ` ` `}` ` ` `else` `{` ` ` `document.write( ` `"No"` `);` ` ` `}` `// This code contributed by Rajput-Ji` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.