Fibonacciness

[David W. Wilson]

For a, b > 0, define the "reverse Fibonacci sequence" R(a, b) as
follows:

    R(0) = a;  R(1) = b;  R(n+2) = R(n) - R(n-1).

For instance, R(20, 11) is

    20, 11, 9, 2, 7, -5, 12, -17, ...

Now, define f(a, b) to be the element of R(a, b) immediately that
preceeds the first nonpositive element.  Thus f(20, 11) = 7.

Finally, define f(a), the Fibonacciness of a, to be the minimum of
f(a, b) over all b >= 1.  The smaller that f(a) is, the more
Fibonaccilike a is.

Questions:

Let c = (sqrt(5)-1)/2 = .6180339...
Does f(a) = min(f(a, floor(ca)), f(a, ceil(ca)))?

Which numbers have Fibonacciness 1? 2? 3?

What is the smallest number of Fibonacciness n (the answer is
an interesting sequence)?