Possible values of "Dropping time" A102419.

[David Wilson]

Think about it. How can 0 and 1 both be in this sequence?

As I see it, there are four reasonable definitions of the dropping time of n 
based on whether

(a) the number of allowable iterations of the Collatz function is 
nonnegative or positive.

(b) we stop at a number <= n or a number < n.

If we allow a nonnegative number of iterations, and stop when we reach a 
number <= n, 0 is the only possible stopping time for any number. If we 
require a positive number of iterations, or we stop when we reach a number < 
n, the possible stopping times are

    1, 3, 6, 8, 11, ...

and, in particular, 0 is not a permissible stopping time. For this reason, I 
think 0 should not appear in this sequence.

I lean towards defining the dropping time as the smallest positive number of 
iterations that results in a number <= n. This way, the dropping time of 1 
is defined (it is 3). If we stop when we reach a number < n, the dropping 
time of 1 is undefined (icky). I really think A074473 is all wrong and 
should be fixed. I will submit a potential fix when I have time.