Suggests is not demands. If we discard the requirement to be an increasing function, one recursively defined solution takes f(3x + 1) = 3x + 2, f(3x + 2) = 3 *

Suggests is not demands. If we discard the requirement to be an increasing function, one recursively defined solution takes f(3x + 1) = 3x + 2, f(3x + 2) = 3 * (3x + 1), and f(3x) = 3f(x), with f(0) = 0. Or analogously for any way of splitting the positive integers not divisible by 3 into ordered pairs (a, b). Then define f(3^n a) = 3^n b and f(3^n b) = 3^(n + 1) a. This is the general form of the solutions.