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December 7[edit]

What does this mean?[edit]

Hi, on the second page of the link below, what does it mean by "The different strings of first digits associated with powers of 2 in a base 10 representation are {1, 2, 4, 8}, {1, 2, 4, 9}, {1, 2, 5}, {1, 3, 6}, {1, 3, 7}"?

http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a7b_896.pdf — Preceding unsigned comment added by 86.169.185.33 (talk) 00:26, 7 December 2014 (UTC)[reply]

It's the possibilities for the first digit of consecutive powers of 2 when you begin at some power starting with the digit 1 (not necessarily 2⁰ = 1) and stop right before the next power starting with 1. Here are examples of what the first two digits could have been in each of the five possible cases: {10, 20, 40, 80}, {12, 24, 48, 96}, {14, 28, 56}, {16, 32, 64}, {18, 36, 72}. PrimeHunter (talk) 00:49, 7 December 2014 (UTC)[reply]

I see, thanks, is it possible from this and the formula that follows to determine the limiting distribution of the first digits of all the powers of 2 (i.e. 2, 4, 8, 16, 32, 64, 128, and so on indefinitely)? I can't seem to get my head round what is being described. 86.169.185.33 (talk) — Preceding undated comment added 01:16, 7 December 2014 (UTC)[reply]