Timeline for Normality property of powers of integers?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 25, 2014 at 14:15 | vote | accept | Per Alexandersson | ||
| Jun 28, 2014 at 3:29 | comment | added | Bill Mance | @Lucia oops I see. I misread it as "there are infinitely many powers of 2 with a zero in their base 10 expansion". GeraldEdgar: Lucia answered your question, but I want to add further this useful resource benfordonline.net | |
| Jun 28, 2014 at 2:50 | comment | added | Lucia | @BillMance: Benford's law (which is simply the equidistribution of $n\log_{10} 2$ in ${\Bbb R}/{\Bbb Z}$) will tell you that given any initial pattern of digits there are many $n\le N$ with $2^n$ beginning with that pattern. It does not say anything about the decimal digits of $2^n$ for every value of $n$, which is the problem raised here (and in Gerry Myerson's comment). | |
| Jun 28, 2014 at 2:09 | comment | added | Gerald Edgar | Reference that $2^n$ follows Benford's law? | |
| Jun 28, 2014 at 1:39 | comment | added | Bill Mance | I might be missing something simple, but doesn't the fact that the sequence $(2^n)$ follows Benford's law in base $10$ give you some things like this? | |
| Jun 28, 2014 at 1:34 | answer | added | Bill Mance | timeline score: 2 | |
| Jun 27, 2014 at 22:55 | comment | added | Gerry Myerson | I'm sure it's true, and I'm sure that far weaker statements are out of reach. So far as I know, there isn't even a proof that every sufficiently large power of 2 has a zero somewhere in its base-10 expression. | |
| Jun 27, 2014 at 22:08 | history | asked | Per Alexandersson | CC BY-SA 3.0 |