# Program to find Star number

A number is termed as star number, if it is a centered figurate number that represents a centered hexagram (six-pointed star) similar to chinese checker game. The few star numbers are 1, 13, 37, 73, 121, 181, 253, 337, 433, ….

Examples:

```Input : n = 2
Output : 13

Input : n = 4
Output : 73

Input : n = 6
Output : 181
```

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

If we take few examples, we can notice that the n-th star number is given by the formula:

`n-th star number = 6n(n - 1) + 1 `

Below is the implementation of above formula.

## C++

 `// C++ program to find star number ` `#include ` `using` `namespace` `std; ` ` `  `// Returns n-th star number ` `int` `findStarNum(``int` `n) ` `{ ` `    ``return` `(6 * n * (n - 1) + 1); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 3; ` `    ``cout << findStarNum(n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find star number ` `import` `java.io.*; ` ` `  `class` `GFG { ` `    ``// Returns n-th star number ` `    ``static` `int` `findStarNum(``int` `n) ` `    ``{ ` `        ``return` `(``6` `* n * (n - ``1``) + ``1``); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``3``; ` `        ``System.out.println(findStarNum(n)); ` `    ``} ` `} ` ` `  `// This code is contributed ` `// by Nikita Tiwari. `

## Python3

 `# Python3 program to ` `# find star number ` ` `  `# Returns n-th  ` `# star number ` `def` `findStarNum(n): ` ` `  `    ``return` `(``6` `*` `n ``*` `(n ``-` `1``) ``+` `1``) ` ` `  `# Driver code ` `n ``=` `3` `print``(findStarNum(n)) ` ` `  `# This code is contributed by Smitha Dinesh Semwal `

## C#

 `// C# program to find star number ` `using` `System; ` ` `  `class` `GFG { ` `    ``// Returns n-th star number ` `    ``static` `int` `findStarNum(``int` `n) ` `    ``{ ` `        ``return` `(6 * n * (n - 1) + 1); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 3; ` `        ``Console.Write(findStarNum(n)); ` `    ``} ` `} ` ` `  `// This code is contributed ` `// by vt_m. `

## PHP

 ` `

Output :

```37
```

Interesting Properties of Start Numbers:

1. The digital root of a star number is always 1 or 4, and progresses in the sequence 1, 4, 1.
2. The last two digits of a star number in base 10 are always 01, 13, 21, 33, 37, 41, 53, 61, 73, 81, or 93.
3. The generating function for the star numbers is
`x*(x^2 + 10*x + 1) / (1-x)^3 = x + 13*x^2 + 37*x^3 +73*x^4 .......`
4. The star numbers satisfy the linear recurrence equation
`S(n) = S(n-1) + 12(n-1)`

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Improved By : jit_t

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