Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
It 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
It's to help Norwegian school children remember which year Henrik Ibsen was born. – Per Manne Oct 21 '12 at 18:02
To misquote Tom Hanks: There's no whying in mathematics. – Ross Millikan Oct 21 '12 at 18:17
"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 ( – Jair Taylor Oct 21 '12 at 18:52
@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
up vote 7 down vote accepted

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.