Dungeon Numbers - Numberphile

Featuring Neil Sloane from the OEIS.

NUMBERPHILE

Videos by Brady Haran
Animation by Pete McPartlan

[PTFVBVB]

There's something about Neil's voice that has a "teacher that really cares about your learning" quality to it

[homegronhomestead]

You should switch from calling it 'dungeons' to 'BASEments'

[Henrix]

How about
...
12
11
10
11
12
...

[otakuribo]

There's a valuable treasure awaiting brave adventurers at the bottom of this dungeon, and his name is Neil Sloane

[Adam-dsik]

Props to the editors and animators. This was pretty dense but their help made it understandable

[ncot_tech]

New mathematical terms here - “pretty big”, “gigantic” and “really tiny”.

[wylandr]

If you listen to this without watching, it's like a madman just rattling off numbers.

[unnamed]

2:22
Took me a while to figure out that 11 was actually an equal sign rotated 270 degrees.







because who says 90 degrees these days

[sbmathsyt]

Never heard of this but that is what is so great about this channel, always bringing fascinating new concepts to the viewers attention. This has certainly inspired me to look more into different bases.

[JSLing-vvgo]

Sloane is great. I love integer sequences.

[captdeadfool]

I got no idea wtf you're talking about but i like how you write stuffs on that brown papers

[abogmus]

Neil sounds like a Half Life scientist

[BrianShelfPartTwo]

Every time I see Mr Sloane's videos I can't take my eyes off his folders. Please can I ask, what are "Fat Struts" ? Thanks for the content y'all.

[LeoStaley]

If number explanations at the online encyclopedia of integer sequences (oeis) were like this, I would spend more time exploring it.

[GhilesNc]

7:01 : You forgot the paper change music !

[dustysparks]

So the "magic jump" in these sequences happens when the second units number increases from 1 to 2 (ie "10 sub x" to "20 sub x")

[noidea]

At first I was like "wait, this is a really simple pattern, 10, 11, 13, 16, 20... that just means that I have to add 1 the first time, 2 the second time, 3 the third time and so on and so on".
But then I saw the numbers at 6:13. Oh boy was I wrong. This pattern is not as simple as I thought.

[nilsragnar]

Neil Sloane might be my favorite guest on Numberphile, glad to have him back!

[Npvsp]

His voice and tone are so relaxing and mesmerising!!

[JovianCloudfarmer]

This does still end up pretty base 10-centric, even though it plays with many different bases. I looked a little into how it ends up when you keep it all in binary and only convert to base 10 at the very end, and it was pretty interesting, since for example, the 4th step is no longer 10_11_12_13, it's 10_11_100_101. The introduction of a third digit in the base so quickly means that you start to square numbers in the base conversion process sooner, so the numbers start to grow bigger sooner. However, since it's powers of 2 and not powers of 10, I suspect that the size of the growth rate changes will be smaller, so it's very possible that base 10 will catch up in terms of number size after a number of steps.
An example (using bottom-up parentheses):
Base 10, 7th step: 10_11_12_13_14_15_16 = 31
Base 2, 7th step: 10_11_100_101_110_111_1000 = A 68-digit binary number, 193825204350418564226 in base 10