Is there any explanation why the block $1828$ occurs twice in the decimal expansion of the transcendental $e$, $2.718281828459\ldots$, but is not recurring?
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2$1828$ cannot be recurring since $e$ is transcendental. – Oct 21 '12 at 17:55
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6It also have 459045 which could be misleading. I like to recite the first decimals of $e$ because they are easier to memorize than $\pi$'s :) – Jean-Sébastien Oct 21 '12 at 17:57
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3And guess what, Euler started to use the letter $\mathrm e$ for the constant in 1727 or 1728! – joriki Oct 21 '12 at 18:02
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14It's to help Norwegian school children remember which year Henrik Ibsen was born. – Per Erik Manne Oct 21 '12 at 18:02
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2The comment of joriki is making me paranoid. Jasper is onto something. – JT_NL Oct 21 '12 at 18:05
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7To misquote Tom Hanks: There's no whying in mathematics. – Ross Millikan Oct 21 '12 at 18:17
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7"I call it contingent beauty. Why do four colors suffice? Just Because!. Why is the Optimal Packing of 3D oranges face-centric cubic? Just Because!. Why is 25 the smallest size of a party in which you are guaranteed that either you can find five people who mutually love each other or four people who mutually hate each other? Just Because! Why are (decimal) digits 3-6 identical with digits 7-10 of e? Just Because!" - Doron Zeilberger (http://www.math.rutgers.edu/~zeilberg/Opinion90.html) – Jair Taylor Oct 21 '12 at 18:52
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3We use the decimal (base ten) system because of a biological fluke and so shouldn't get too excited when we see something like this. There are plenty of other bases available in which $e$ doesn't have a pair of matching strings near the start. – Peter Phipps Oct 21 '12 at 19:00
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5@Peter: On the other hand, $[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,\dots]$. – Brian M. Scott Oct 21 '12 at 19:13
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4How many copies would you prefer? – Will Jagy Oct 21 '12 at 19:24
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1@Jair. More pithily, Chaitin said, "some things are true for no reason." – Rick Decker Oct 21 '12 at 23:35
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4One of the convergents is 2721/1001. – i. m. soloveichik Oct 22 '12 at 01:45
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@RossMillikan: I beg to differ. This answer of yours is about the whys. – P.K. Nov 20 '12 at 14:28
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interesting; I never noticed that before! – amWhy Nov 21 '12 at 00:08
1 Answers
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I don't believe this question has a good answer, as I don't believe this repetition is very significant.
Similarly, the $762^{\text {nd}}$ digit of $\pi$ begins the Feynman point, a sequence of six $9s$ (Feynman stated he wanted to memorize until this point, so he could recite the digits, ending with "nine nine nine nine nine nine, and so on").
This sequence of numbers in $\pi$ is similarly strange, however, it seems like this is simply a string of numbers that happened to be arranged this way in base $10$ and is a rather insignificant coincidence.
Argon
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