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# 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```

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

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## Javascript

 ``

Output :

`37`

Time complexity: O(1) since performing constant operations

Space complexity: O(1) since using constant variables

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 .......`
1. The star numbers satisfy the linear recurrence equation

`S(n) = S(n-1) + 12(n-1)`

References :
http://mathworld.wolfram.com/StarNumber.html
https://en.wikipedia.org/wiki/Star_number
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