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 = 6

Output:Yes

Explanation:

Second Centered pentagonal number is 6.

Input:N = 20

Output:No

**Approach:**

- The
**K**term of the Centered Pentagonal Number is given as^{th} - As we have to check that the given number can be expressed as a Centered Pentagonal Number or not. This can be checked as:

=>

=> - If the value of
**K**calculated using the above formula is an integer, then**N**is a Centered Pentagonal Number. - 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; ` `} ` |

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## 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 ` |

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## 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` |

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## 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 ` |

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**Output:**

Yes

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