I'm not sure I entirely understand the question, but does this solve the problem?

In[252]:= Table[Floor[Floor[Sqrt[2^n], 0.1]], {n, 1., 10.}]

Out[252]= {1, 2, 2, 4, 5, 8, 11, 16, 22, 32}

UPDATE: I read the Wikipedia page on f-stops, and I think I now understand the problem. Does this work?

Grid[{{"AV"}~Join~Table[av, {av, 10}], {"f/No."}~Join~

Table[N[Sqrt[2]^av, 2], {av, 10}]}, Frame -> All]

(It doesn't use Floor, but it works.)

-Jesse