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Program to find Star number
• Difficulty Level : Medium
• Last Updated : 05 Apr, 2021

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

 ``

## Javascript

 ``

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 .......`
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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