Question: I'm working on a problem that asks to generate a sequence using prime numbers 2, 3, and 5, and then displaying then nth number in the sequence. So, if I ask the program to display the 1000th number, it should display it.

I can't be using arrays or anything like that, just basic decisions and loops.

I started working on it and hit a wall... here's what I got:

```
#include <iostream>

using namespace std;
int main() {
    unsigned int n=23;
    for(int i=2; i<n; i++){
        if(i%2==0){
            cout<<i<<", ";
        }else if(i%3==0){
            cout<<i<<", ";
        }else if(i%5==0){
            cout<<i<<", ";
        }
    }

    return 0;
}

```

Unfortunately, that code doesn't do what's required. It displays numbers such as 14, which includes a prime number 7.... The numbers can only be divided by the 3 specified primes (2,3,5).

I found some information that I'm trying to understand, and so far not sure how to implement it... maybe using lots of for() loops? So, it appears I have to use the concept of 2^n \* 3^m \* 5^k where n+m+k>0.

I guess I have to run a number through a test where it checks to see first if it's fully divisible by 2^1 \* 3^0 \* 5^0, then 2^0 \* 3^1 \* 5^0, then 2^0 \* 3^0 \* 5^1, and so on... Just not sure where to begin.

Answer: 
This code will do it. Breaking a problem down into smaller problems is often a good plan.

```
int main() {
    unsigned int n=23;

    unsigned int counter=0;
    unsigned int answer;
    for ( answer = 2; counter < n; ++answer ) {
        if ( isNotDivisibleByAPrimeGreaterThan5( i ) {
           ++counter;
        }
    }
    cout << answer;
    return 0;
}

```

Now you only have to write this function.

```
bool isNotDivisibleByAPrimeGreaterThan5( unsigned int i ) {
  // return true if i is not divisable by a prime greater than 5.
}

```
Check this. 

```
#include <iostream>
using namespace std;

int IsPrime(int var);
int CheckifPrimeGreaterThaFive(int Num);
int GetFactors(int Num)
{
    int i =0,j=0;
    for (i =2,j=0; i <= Num; i++)
    {
        if (Num%i == 0)
        {
           if (1 == CheckifPrimeGreaterThaFive(i))
           {
                 return 1;
              }
        }
    }
    return 0;
}

int CheckifPrimeGreaterThaFive(int Num)
{
   if ((Num != 2 && Num != 3 && Num != 5) && IsPrime(Num))
   {

           return 1;
   }

    return 0;
}

int IsPrime(int var)
{
    for (int i = 2; i <= var/2; i++)
    {
        if (var % i == 0)
           return 0;
    }
    return 1;
}

int main() {
    int n=98;
    int i, FactorsCount=0;

    for(i=2; i<n; i++)
    {
        if (0 == GetFactors(i))
        {  
           cout<<" "<<i;
        }   
    }
    return 0;
}

```