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++

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// 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

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// 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

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# 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#

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// 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

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<?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:

  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)

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

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Improved By : jit_t



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