//(1) Complete the collatz function below. It should

//    recursively calculate the number of steps needed 

//    until the collatz series reaches the number 1.

//    If needed you can use an auxilary function that

//    performs the recursion. The function should expect

//    arguments in the range of 1 to 10 Million.

def collatz(n: Long): List[Long] =

  if (n == 1) List(1) else

    if (n % 2 == 0) (n::collatz(n / 2)) else 

      (n::collatz(3 * n + 1))

//(2)  Complete the collatz bound function below. It should

//     calculuate how many steps are needed for each number 

//     from 1 upto a bound and return the maximum number of

//     steps. You should expect bounds in the range of 1

//     upto 10 million. 

// some testing harness