fair_distributions_naive_imp <- function(k) {
    count <- 0
    iterations = 0
    for (n in 1:k) {
      for (m in n:k) {
       iterations = iterations + 1
       if (is_fair_distribution(n, m)) {
          count = count + 2
          break
       }
    }
  }
  count
  iterations
}

powers <- c(1, 2, 3, 4, 5,10)
powers.low <- c(1, 2, 3, 4)
for (p in powers){
 print(fair_distributions_naive_imp(10^p))
}