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 <bits/stdc++.h>` `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

`<?php` `//PHP program to find star number` `// Returns n-th star number` `function` `findStarNum(` `$n` `)` `{` ` ` `return` `(6 * ` `$n` `* (` `$n` `- 1) + 1);` `}` `// Driver code` `$n` `= 3;` `echo` `findStarNum(` `$n` `);` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript program to find star number` `// Returns n-th star number` `function` `findStarNum(n)` `{` ` ` `return` `(6 * n * (n - 1) + 1);` `}` `// Driver code` `let n = 3;` `document.write(findStarNum(n));` `// This code is contributed by rishavmahato348.` `</script>` |

**Output :**

37

**Interesting Properties of Start Numbers: **

- The digital root of a star number is always 1 or 4, and progresses in the sequence 1, 4, 1.
- 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.
- 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 .......

- 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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