f(n) for n = 4 .. 44 : 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 dips f(n+1) < f(n): none plateaus R(s+1) = R(s): [(1, 4)] -> predicted dips at n = R - 1: [3] (only n >= 4 is in range) f(n) >= sqrt(n) + 1 at: [(15, 5, 4.873), (16, 5, 5.0), (34, 7, 6.831), (35, 7, 6.916), (36, 7, 7.0)] f(n) <= sqrt(n) + 1 everywhere: False