Vivaldi number

Question

The Vivaldi number is a number that can only be taken into account 2, 3 and 5. ( V = 2^a * 3^b * 5^c, a, b, c = 0,1,...). The task is to find the number of the Nth Vivaldi number. The algorithm is not so bad for small inputs, but N ranges from 0 to 9999. It took 2 minutes in 2000. I wrote code with a fairly simple algorithm, but I am curious (hopeless) to find another way. I tried to solve the problem mathematically using logarithms, but nowhere is it. An effective way is even possible when it comes to large entrances?

#include <iostream>
#include <cstdlib>
#include <ctime>


bool vivaldi(unsigned long long d) {

    while (d%2 == 0)
        d = d/2;

    while (d%3 == 0)
        d = d/3;

    while (d%5 == 0)
        d = d/5;


    if (d == 1)
        return true;

    return false;
}



int main() {

    int count = 0, N;
    unsigned long long number = 0;

    std::cin >> N;

    std::clock_t begin = clock();

    if (N < 0 || N > 9999) {
        std::fprintf(stderr, "Bad input\n");
        std::exit(EXIT_FAILURE);
    }

    while (count <= N) {

        number++;
        if (vivaldi(number))
            count++;

    }

    std::cout << number << std::endl;
    std::clock_t end = clock();
    double elapsed_secs = double(end - begin) / CLOCKS_PER_SEC;
    std::cout << "TIME: " << elapsed_secs << std::endl;
}