# Program to check if N is a Star Number

Given an integer N, the task is to check if it is a star number or not.

Star number is a centered figurate number that represents a centered hexagram (six-pointed star) similar to Chinese checker game. The first few Star numbers are 1, 13, 37, 73 …

Examples:

Input: N = 13
Output: Yes
Explanation:
Second star number is 13.

Input: 14
Output: No
Explanation:
Second star number is 13, where as 37 is third.
Therefore, 14 is not a star number.

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

Approach:

1. The Kth term of the star number is given as 2. As we have to check that the given number can be expressed as a star number or not. This can be checked as follows –

=> => => 3. Finally, check the value of computed using this formulae is an integer, which means that N is a star number.

Below is the implementation of the above approach:

## C++

 // C++ implementation to check that  // a number is a star number or not     #include     using namespace std;     // Function to check that the  // number is a star number  bool isStar(int N)  {      float n          = (6 + sqrt(24 * N + 12))            / 6;         // Condition to check if the      // number is a star number      return (n - (int)n) == 0;  }     // Driver Code  int main()  {      int i = 13;         // Function call      if (isStar(i)) {          cout << "Yes";      }      else {          cout << "No";      }      return 0;  }

## Java

 // Java implementation to check that  // a number is a star number or not  import java.io.*;   import java.util.*;      class GFG{          // Function to check that the  // number is a star number  static boolean isStar(int N)  {      double n = (6 + Math.sqrt(24 * N + 12)) / 6;         // Condition to check if the      // number is a star number      return (n - (int)n) == 0;  }         // Driver code  public static void main(String[] args)   {       int i = 13;         // Function call      if (isStar(i))      {          System.out.println("Yes");      }      else      {          System.out.println("No");      }  }   }      // This code is contributed by coder001

## Python3

 # Python3 implementation to check that   # a number is a star number or not   import math     # Function to check that the   # number is a star number   def isStar(N):             n = (math.sqrt(24 * N + 12) + 6) / 6            # Condition to check if the       # number is a star number      return (n - int(n)) == 0        # Driver Code   i = 13    # Function call  if isStar(i):      print("Yes")  else:      print("No")     # This code is contributed by ishayadav181

## C#

 // C# implementation to check that  // a number is a star number or not  using System;     class GFG{          // Function to check that the  // number is a star number  static bool isStar(int N)  {      double n = (6 + Math.Sqrt(24 * N + 12)) / 6;         // Condition to check if the      // number is a star number      return (n - (int)n) == 0;  }         // Driver code  public static void Main()   {       int i = 13;         // Function call      if (isStar(i))      {          Console.WriteLine("Yes");      }      else     {          Console.WriteLine("No");      }  }   }      // This code is contributed by Code_Mech

Output:

Yes


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