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?
Why decimal expansion of $e$ has two copies of $1828$
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$\begingroup$
exponential-function
decimal-expansion
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2$1828$ cannot be recurring since $e$ is transcendental. – 2012-10-21
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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 :) – 2012-10-21
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3And guess what, [Euler started to use the letter $\mathrm e$ for the constant in 1727 or 1728](http://en.wikipedia.org/wiki/E_%28mathematical_constant%29#History)! – 2012-10-21
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13It's to help Norwegian school children remember which year Henrik Ibsen was born. – 2012-10-21
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2The comment of joriki is making me paranoid. Jasper is onto something. – 2012-10-21
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7To misquote Tom Hanks: There's no whying in mathematics. – 2012-10-21
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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) – 2012-10-21
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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. – 2012-10-21
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5@Peter: On the other hand, $[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,\dots]$. – 2012-10-21
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4How many copies would you prefer? – 2012-10-21
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1@Jair. More pithily, Chaitin said, "some things are true for no reason." – 2012-10-21
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3One of the convergents is 2721/1001. – 2012-10-22
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0@RossMillikan: I beg to differ. [This answer of yours](http://math.stackexchange.com/questions/9286/proving-int-0-infty-e-x2-dx-frac-sqrt-pi2/9292#9292) *is* about the *whys*. – 2012-11-20
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0interesting; I never noticed that before! – 2012-11-21
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.