# 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 <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; ` `} ` |

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## 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. ` |

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## 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 ` |

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## 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. ` |

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## 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 ` `?> ` |

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**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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