Generar una lista de n números compuestos consecutivos (Un método interesante)

Dado un número n, genera una lista de n números compuestos .
Ejemplos: 
 

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

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

La idea aquí es usar las propiedades de  . Ya que  , entonces los números  , todos se dividen  . Por  lo tanto es divisible por 2,  es divisible por 3…..  es divisible por n. Y según el patrón anterior, son compuestos consecutivos.
¡Encontramos (n+1)!, luego imprimimos números (n+1)! + 2, (n+1)! + 3, …. (n+1)! + (n + 1).
A continuación se muestra la implementación del enfoque anterior:
 

// 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 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 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# 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 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.
?>

<script>
 
// JavaScript program to print n consecutive composite
// numbers
 
// function to find factorial of given
// number
    function factorial(n) {
        let res = 1;
        for (let i = 2; i <= n; i++) {
            res *= i;
        }
        return res;
    }
   
// Prints n consecutive numbers.
    function printNComposite(n) {
        let fact = factorial(n + 1);
        for (let i = 2; i <= n + 1; ++i) {
            document.write(fact + i + " ");
        }
    }
 
// Driver code
     
        let n = 4;
        printNComposite(n);
     
    // This code is contributed by code_hunt.
</script>

122 123 124 125

La solución anterior provoca un desbordamiento muy pronto (para valores pequeños de n). Podemos usar la técnica para encontrar un factorial de gran número para evitar el desbordamiento.