There is a standard problem to show that the distribution of leading digits of $2^n$ is that the digit $k$ occurs with the frequency $\log_{10}(k+1)-\log_{10}(k)$. (This easily generalises to other bases --- though base 2 is rather pointless!)

Since Fibonacci is also ``exponential except for an error term''. Is this true for that as well --- or does the error term make it fail?

leadingdigit? – Qiaochu Yuan Feb 6 '12 at 17:54