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.

By the way, the previous approximation is more old-fogey thinking.  30.1% of the length of my trusty slide rule is dedicated to numbers whose leading digits are 1.  Of course, I can only do approximations with my slide rule.  Probably why it was replaced by computers.

Posted by Steve Herman on 2011-02-18 14:00:31