Yes, this is off because x is a function from natural numbers to natural numbers; it is not a number. Thus, x(19) is a number, but 2x and 38x don't make sense.2x(19) - 1 = 38x - 1 which seems completely off?

I'll write the argument of x as a subscript: instead of . By definition, . After that, the first idea that came to mind was to guess the general formula for by calculating the first several values of and, possibly, to prove this general formula by induction.

Can you guess the general formula for ?