I want to map integers on [0, ?) to [0, 1], so that 1/f'(x) * f(x±h) is as close as possible to 1/x' * x±h.
How do I accomplish this? Setting f(x) = 1-1/(log(log(log(log(x+1)+1)+1)+1)+1) turned out quite well in my simulations, but is there a better way?
How do I accomplish this? Setting f(x) = 1-1/(log(log(log(log(x+1)+1)+1)+1)+1) turned out quite well in my simulations, but is there a better way?
