# 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 numberis 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.

**Approach:**

- The K
^{th}term of the star number is given as - As we have to check that the given number can be expressed as a star number or not. This can be checked as follows –

=>

=>

=> - 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 <bits/stdc++.h> ` ` ` `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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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**Output:**

Yes

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