OK, this has nothing to do with climate. But it's connected with the trends gadget. I made a nudger that looked like this <<<<>>>>. If you click on the center symbols, you nudge by one month. Next out by 2, then four, and in this version, the outermost move by 8.
Well, suppose the sequence of symbols continued, in powers of 2, as far as needed. How far can you be sure of being able to move with, say, 2, 3, 4 or 5 clicks. More precisely, what is the least number that requires n clicks.
For n=2, it's 3. For n=3 it's 11 (8+2+1 or 16-4-1). But 4? 5? Can anyone think of a rule?
I can think of an upper bound for any n. It's less that 4^(n-1). But not a general formula.