It is known that the function f (x) is a monotone increasing function defined on (0, + ∞). When n ∈ n *, f (n) ∈ n *, if f [f (n)] = 3N, then the value of F (5) is equal to______ ．

It is known that the function f (x) is a monotone increasing function defined on (0, + ∞). When n ∈ n *, f (n) ∈ n *, if f [f (n)] = 3N, then the value of F (5) is equal to______ ．

If f (1) = 1, then f (f (1)) = f (1) = 1, which is contradictory to the condition f (f (n)) = 3N, it is not tenable; if f (1) = 3, then f (f (1)) = f (3) = 3, and then f (f (3)) = f (3) = 9, which is contradictory to the former formula, it is not tenable; if f (1) = n (n > 3), then f (f (1)) = f (n) = 3, which is contradictory to f (x) monotonically increasing, so only f (1) = 2 (1) ) = f (2) = 3, then f (f (2)) = f (3) = 6, then f (f (3)) = f (6) = 9, by monotonicity, f (4) = 7, f (5) = 8, so the answer is: 8