1, 2, 4, 8, 1, 3, 6, 1 ... is a non-cyclic series where a(n) represents the leading digit of 2^n.

a) How many ones are there within the first 3000 members?

b) Same question for a digit d, other than digit one.

Solution can be approximated by Benford's law (my favorite law).

Approximation is 3000*(log(d+1)-log(d)) where log is log base 10

For part a, this gives about 30.1%*3000 = 903.

I'm curious to see how closely this matches the actual answer.

(By the way, have I mentioned that 30% of all base 10 numbers have the digit 1 as their first significant digit?).