Roger Hui: In the year 2033 Earth was discovered by Survey Fleet MCXII of the Galactic Empire. The Emperor ordered Earth to send a representative to the court, with strict instructions to “bring something beautiful”.

Emperor: What beautiful things does Earth have?

Earth Representative: Your excellency, our mathematician Euler proved in our year 1737 that +/(1+⍳∞)-s ←→ ×/÷1-(⍭⍳∞)-s

Emperor: What is the ⍭ symbol?

Earth Rep.: ⍭i is the i-th prime.

Emperor: And what is ∞? Does it do anything useful?

Earth Rep.: It denotes infinity, your excellency.

Emperor: (ponders equation for a minute or two) Respect!

Emperor: Neat notation you have there. Tell me more.

Earth Rep.: Your excellency, it’s called APL. It was invented by the Canadian Kenneth E. Iverson …

Still not sure what i and 17 are...

its a joke about how Euler's identity isn't normally simplified and written as:

     E^(iπ) = -1 

because people wanna be "cute" about it containing 0 and 1, so why not a bunch of other arbitrary numbers too?

Setting an expression equal to 0 is quite standard form.

Number i is the complex unit, but I've no idea about 17 either.

It's the first arbitrary number. 4711 is the second arbitrary number. They were used as the numeric foo and bar when I studied programming in high school and college during the 90s. I always thought it was universal hackerdom, but I actually rarely see them referenced. Perhaps it's a European thing?

Do you have a source on "arbitrary number"? There were no obvious explanations online.

It's not a mathematical or in any way strict thing. It's just a number chosen to exemplify any number. Just like "foo", "bar", "baz", "qux", etc, a sequence of numbers could be e.g. 17, 42, 4711. I grew up with it, and googling it seems that at least 4711 is a German thing.

I was thinking, what is the smallest number not found in any sequence on https://oeis.org/?

17 is the favorite number of David Kelly, a mathematician and professor of Hampshire College. He loves it for a very large number of reasons. He was instrumental in creating a summer camp at Hampshire which has trained many young brilliant mathematical minds. (Including Vi Hart). Thus it has spread.

http://www.vinc17.net/yp17/index.en.html

Following the links from that link, I find wikipedia for 17 says, "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygons) could be constructed with ruler and compasses."

(I learned it as straightedge and compass.) Wikipedia did not mention the story that Gauss has a regular heptadecagon inscribed on his tombstone.

You can find such "collections" for numbers like 7, 8, or 13, even ignoring the integers 0-4, and 42 is obviously a reference to Hitchhikers guide, a work of fiction. Am I missing something?

Surely he loves it for 17 reasons.

i= sqrt(-1)

https://en.wikipedia.org/wiki/Euler%27s_identity