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
The idea here is using the properties of 
. Since 
, then numbers 
, all divide . Therefore 
is divisible by 2, 
is divisible by 3 ….. 
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. ?> |
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.
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