Based on the given information, it appears that the rule is to add 3 to the previous number in the sequence. For example, 1 + 3 = 4, but since 1 is mapped to 5, we add an additional 1 to get 5. Similarly, 2 + 3 = 5, but since 2 is mapped to 8, we add an additional 3 to get 8. Following this pattern, we can see that 3 + 3 = 6, but since 3 is mapped to 11, we add an additional 5 to get 11. Therefore, the rule seems to be f(x) = x + (x + 2), where x is the input number and f(x) is the output number.
Using this rule, we can determine that f(16) = 16 + (16 + 2) = 16 + 18 = 34. However, according to the information given in the question, f(16) = 50, which does not match our calculated value. So it seems that the rule does not hold for all values in the sequence.