Generate a list of n consecutive composite numbers (An interesting method)

Given a number n, generate a list of n composite numbers.

Examples:

Input : 5
Output : 122, 123, 124, 125

Input : 10
Output : 3628802, 3628803, 3628804, 3628805, 3628806, 
         3628807, 3628808, 3628809, 3628810

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea here is using the properties of $n!$ . Since $n! = 1\times2\times3....(n-1)\times n$ , then numbers $1, 2, 3..... (n-1), n$ , all divide $n!$ . Therefore $n!+2$ is divisible by 2, $n!+3$ is divisible by 3 ….. $n!+n$ is divisible by n. And by above pattern they are consecutive composites.

We find (n+1)!, then we print numbers (n+1)! + 2, (n+1)! + 3, …. (n+1)! + (n + 1).

Below is the implementation of above approach:

C++

// CPP program to print n consecutive composite 
// numbers. 
#include <iostream> 
using namespace std; 
  
// function to find factorial of given  
// number 
unsigned long long int factorial(unsigned int n) 
{     
    unsigned long long int res = 1; 
    for (int i=2; i<=n; i++) 
        res *= i; 
    return res; 
} 
  
// Prints n consecutive numbers.  
void printNComposite(int n) 
{ 
    unsigned long long int fact = factorial(n+1); 
    for (int i = 2; i <= n+1; ++i)  
        cout << fact + i << " ";  
} 
  
// Driver program to test above function 
int main() 
{ 
    int n = 4; 
    printNComposite(n); 
    return 0; 
} 

Java

// Java program to print n consecutive composite  
// numbers 
  
class GFG { 
  
// function to find factorial of given  
// number  
    static long factorial(int n) { 
        long res = 1; 
        for (int i = 2; i <= n; i++) { 
            res *= i; 
        } 
        return res; 
    } 
  
// Prints n consecutive numbers.  
    static void printNComposite(int n) { 
        long fact = factorial(n + 1); 
        for (int i = 2; i <= n + 1; ++i) { 
            System.out.print(fact + i + " "); 
        } 
    } 
  
// Driver program to test above function  
    public static void main(String[] args) { 
        int n = 4; 
        printNComposite(n); 
  
    } 
} 

Python3

# Python3 program to print n consecutive 
# composite numbers. 
  
# function to find factorial  
# of given number 
def factorial( n): 
  
    res = 1; 
    for i in range(2, n + 1): 
        res *= i; 
    return res; 
  
# Prints n consecutive numbers.  
def printNComposite(n): 
    fact = factorial(n + 1); 
    for i in range(2, n + 2):  
        print(fact + i, end = " ");  
  
# Driver Code 
n = 4; 
printNComposite(n); 
      
# This code is contributed by mits 

C#

// C# program to print n consecutive composite  
// numbers 
using System; 
                      
public class Program{ 
   
// function to find factorial of given  
// number  
    static long factorial(int n) { 
        long res = 1; 
        for (int i = 2; i <= n; i++) { 
            res *= i; 
        } 
        return res; 
    } 
   
// Prints n consecutive numbers.  
    static void printNComposite(int n) { 
        long fact = factorial(n + 1); 
        for (int i = 2; i <= n + 1; ++i) { 
            Console.Write(fact + i + " "); 
        } 
    } 
   
// Driver program to test above function  
    public static void Main() { 
        int n = 4; 
        printNComposite(n); 
   
    } 
} 
  
// This code is contributed by Rajput-Ji 

PHP

<?php 
// PHP program to print n consecutive 
// composite numbers. 
  
// function to find factorial of given  
// number 
function factorial( $n) 
{  
    $res = 1; 
    for ($i = 2; $i <= $n; $i++) 
        $res *= $i; 
    return $res; 
} 
  
// Prints n consecutive numbers.  
function printNComposite(int $n) 
{ 
    $fact = factorial($n + 1); 
    for($i = 2; $i <= $n + 1; ++$i)  
        echo $fact + $i ," ";  
} 
  
    // Driver Code 
    $n = 4; 
    printNComposite($n); 
      
// This code is contributed by anuj_67. 
?> 

Output:

122 123 124 125

The above solution causes overflow very soon (for small values of n). We can use technique to find factorial of large number to avoid overflow.

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

Recommended Posts: