# Program to check if N is a Centered Pentagonal Number or not

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 Number is 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 are 1, 6, 16, 31, 51, 76, 106 …

Examples:

Input: N = 6
Output: Yes
Explanation:
Second Centered pentagonal number is 6.

Input: N = 20
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. The Kth 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  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

Output:

Yes


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