# Program to check if N is a Centered Decagonal Number

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

Centered Decagonal Number is centered figurative number that represents a decagon with dot in center and all other dot surrounding it in successive Decagonal Number form. The first few Centered decagonal numbers are 1, 11, 31, 61, 101, 151 …

Examples:

Input: N = 11
Output: Yes
Explanation:
Second Centered decagonal number is 11.

Input: N = 30
Output: No

Approach:

1. The Kth term of the Centered Decagonal Number is given as

2. As we have to check that the given number can be expressed as a Centered Decagonal Number or not. This can be checked as follows:

=>
=>

3. If the value of K calculated using the above formula is an integer, then N is a Centered Decagonal Number.

4. Else the number N is not a Centered Decagonal 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 decagonal number bool isCentereddecagonal(int N) {     float n         = (5 + sqrt(20 * N + 5))           / 10;       // Condition to check if N     // is Centered Decagonal Number     return (n - (int)n) == 0; }   // Driver Code int main() {     int N = 11;       // Function call     if (isCentereddecagonal(N)) {         cout << "Yes";     }     else {         cout << "No";     }     return 0; }

## Java

 // Java implementation to check that a number // is a centered decagonal number or not  import java.lang.Math;   class GFG{       // Function to check that the number  // is a centered decagonal number  public static boolean isCentereddecagonal(int N)  {      double n = (5 + Math.sqrt(20 * N + 5)) / 10;        // Condition to check if the number      // is a centered decagonal number      return (n - (int)n) == 0;  }    // Driver Code public static void main(String[] args)  {     int n = 11;        // Function call      if (isCentereddecagonal(n))      {          System.out.println("Yes");     }      else     {          System.out.println("No");     }  } }   // This code is contributed by ShubhamCoder

## Python3

 # Python3 program for the above approach import numpy as np   # Function to check if the number N # is a centered decagonal number def isCentereddecagonal(N):       n = (5 + np.sqrt(20 * N + 5)) / 10       # Condition to check if N      # is centered decagonal number     return (n - int(n)) == 0   # Driver Code  N = 11   # Function call  if (isCentereddecagonal(N)):     print ("Yes")  else:     print ("No")   # This code is contributed by PratikBasu

## C#

 // C# implementation to check that a number // is a centered decagonal number or not  using System;   class GFG{       // Function to check that the number  // is a centered decagonal number  static bool isCentereddecagonal(int N)  {      double n = (5 + Math.Sqrt(20 * N + 5)) / 10;            // Condition to check if the number      // is a centered decagonal number      return (n - (int)n) == 0;  }        // Driver Code static public void Main () {     int n = 11;            // Function call      if (isCentereddecagonal(n))      {          Console.Write("Yes");     }      else     {          Console.Write("No");     }  } }   // This code is contributed by ShubhamCoder

## Javascript

 

Output:

Yes

Time Complexity: O(logn)

Auxiliary Space: O(1)

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