When Benford's law predicts perfectly

When Benford's law predicts perfectly

Eight years ago I wrote a blog post on the Leading digits of powers of 2. In that post I said that Benford’s law gives remarkably good predictions for the distribution of leading digits of 2n. In this post I’ll make that statement stronger. A sequence obeys Benford’s law, in base 10, if the proportion of the first N elements of the sequence that begin with the digit d is asymptotically N log10(1 + 1/d). Benford’s law applies to powers of 2, but …