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a) is easy, b) is not (Posted on 2011-02-18) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (2 votes)

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Some Thoughts approximation (spoiler) | Comment 1 of 8
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?).

  Posted by Steve Herman on 2011-02-18 13:37:33
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