# Program to check if N is a Centered Pentadecagonal Number

Given a number **N**, the task is to check whether **N** is a Centered pentadecagonal number or not. If the number **N** is a Centered Pentadecagonal Number then print **“Yes”** else print **“No”**.

Centered Pentadecagonal Number represents a dot in the centre and other dots surrounding it in successive Pentadecagonal(

15-sided polygon) layers. The first few Centered pentadecagonal numbers are1, 16, 46 …

**Examples:**

Input:N = 16Output:YesExplanation:

Second Centered pentadecagonal number is 16.

Input:N = 20Output:No

**Approach:**

1. The **K ^{th}** term of the Centered pentadecagonal number is given as:

2. As we have to check that the given number can be expressed as a Centered Pentadecagonal 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 Pentadecagonal Number.

4. Else the number **N** is not a Centered Pentadecagonal 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 number N is a` `// Centered Pentadecagonal Number` `bool` `isCenteredpentadecagonal(` `int` `N)` `{` ` ` `float` `n` ` ` `= (16 + ` `sqrt` `(120 * N + 105))` ` ` `/ 30;` ` ` `// Condition to check if N is a` ` ` `// Centered Pentadecagonal Number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given Number` ` ` `int` `N = 16;` ` ` `// Function call` ` ` `if` `(isCenteredpentadecagonal(N)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `class` `GFG{` `// Function to check if number N is a` `// Centered Pentadecagonal Number` `static` `boolean` `isCenteredpentadecagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `)(` `16` `+ Math.sqrt(` `120` `* N +` ` ` `105` `)) / ` `30` `;` ` ` `// Condition to check if N is a` ` ` `// Centered Pentadecagonal Number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `// Given Number` ` ` `int` `N = ` `16` `;` ` ` `// Function call` ` ` `if` `(isCenteredpentadecagonal(N))` ` ` `{` ` ` `System.out.println(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by rutvik_56` |

## Python3

`# Python3 program for the above approach` `import` `math` `# Function to check if number N is a` `# centered pentadecagonal number` `def` `isCenteredpentadecagonal(N):` ` ` ` ` `n ` `=` `(` `16` `+` `math.sqrt(` `120` `*` `N ` `+` `105` `)) ` `/` `30` ` ` ` ` `# Condition to check if N is a` ` ` `# centered pentadecagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `N ` `=` `16` `# Function call` `if` `isCenteredpentadecagonal(N):` ` ` `print` `(` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by ishayadav181` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` ` ` `// Function to check if number N is a` `// centered pentadecagonal number` `public` `static` `bool` `isCenteredpentadecagonal(` `int` `N)` `{` ` ` `double` `n = (16 + Math.Sqrt(120 * N +` ` ` `105)) / 30;` ` ` ` ` `// Condition to check if N is a` ` ` `// centered pentadecagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` ` ` `// Given number` ` ` `int` `N = 16;` ` ` ` ` `// Function call` ` ` `if` `(isCenteredpentadecagonal(N))` ` ` `{` ` ` `Console.WriteLine(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.WriteLine(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by divyeshrabadiya07` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to check if number N is a` `// Centered Pentadecagonal Number` `function` `isCenteredpentadecagonal(N)` `{` ` ` `var` `n = (16 + Math.sqrt(120 * N +` ` ` `105)) / 30;` ` ` `// Condition to check if N is a` ` ` `// Centered Pentadecagonal Number` ` ` `return` `(n - (parseInt(n))) == 0;` `}` `// Driver Code` `// Given Number` `var` `N = 16;` `// Function call` `if` `(isCenteredpentadecagonal(N))` `{` ` ` `document.write(` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` `// This code is contributed by Kirti` ` ` `</script>` |

**Output:**

No

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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