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

Centered Pentagonal Numberis a centered figurate number that represents a pentagon with a dot in the centre and other dots surrounding it in pentagonal layers successively. The first few Centered Pentagonal Number are1, 6, 16, 31, 51, 76, 106 …

**Examples:**

Input:N = 6Output:YesExplanation:

Second Centered pentagonal number is 6.

Input:N = 20Output:No

**Approach:**

1. The **K ^{th}** term of the Centered Pentagonal Number is given as

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

4. Else the number **N** is not a Centered Pentagonal 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 pentagonal number` `bool` `isCenteredpentagonal(` `int` `N)` `{` ` ` `float` `n` ` ` `= (5 + ` `sqrt` `(40 * N - 15))` ` ` `/ 10;` ` ` `// Condition to check if N is a` ` ` `// Centered pentagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given Number` ` ` `int` `N = 6;` ` ` `// Function call` ` ` `if` `(isCenteredpentagonal(N)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to check if number N` `// is a centered pentagonal number` `static` `boolean` `isCenteredpentagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `) ((` `5` `+ Math.sqrt(` `40` `* N -` ` ` `15` `)) / ` `10` `);` ` ` `// Condition to check if N is a` ` ` `// centered pentagonal number` ` ` `return` `(n - (` `int` `)n) == ` `0` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given Number` ` ` `int` `N = ` `6` `;` ` ` `// Function call` ` ` `if` `(isCenteredpentagonal(N))` ` ` `{` ` ` `System.out.print(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.print(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by sapnasingh4991` |

## Python3

`# Python3 program for the above approach` `import` `numpy as np` `# Function to check if number N` `# is a centered pentagonal number` `def` `isCenteredpentagonal(N):` ` ` `n ` `=` `(` `5` `+` `np.sqrt(` `40` `*` `N ` `-` `15` `)) ` `/` `10` ` ` `# Condition to check if N is a` ` ` `# centered pentagonal number` ` ` `return` `(n ` `-` `int` `(n)) ` `=` `=` `0` `# Driver Code` `N ` `=` `6` `# Function call` `if` `(isCenteredpentagonal(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 number N` `// is a centered pentagonal number` `static` `bool` `isCenteredpentagonal(` `int` `N)` `{` ` ` `float` `n = (` `float` `) ((5 + Math.Sqrt(40 * N -` ` ` `15)) / 10);` ` ` `// Condition to check if N is a` ` ` `// centered pentagonal number` ` ` `return` `(n - (` `int` `)n) == 0;` `}` `// Driver Code` `public` `static` `void` `Main(` `string` `[] args)` `{` ` ` ` ` `// Given number` ` ` `int` `N = 6;` ` ` `// Function call` ` ` `if` `(isCenteredpentagonal(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 number N` `// is a centered pentagonal number` `function` `isCenteredpentagonal(N)` `{` ` ` `var` `n = ((5 + Math.sqrt(40 * N -` ` ` `15)) / 10);` ` ` `// Condition to check if N is a` ` ` `// centered pentagonal number` ` ` `return` `(n - parseInt(n) == 0);` `}` `// Driver Code` `//Given Number` `var` `N = 6;` `// Function call` `if` `(isCenteredpentagonal(N))` `{` ` ` `document.write(` `"Yes"` `);` `}` `else` `{` ` ` `document.write(` `"No"` `);` `}` `// This code is contributed by Amit Katiyar` `</script>` |

**Output:**

Yes

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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