The Perplexing Patterns of Palindromic Numbers

Follow me into the realm of "palindromic numbers", where we'll investigate the strange traits of palindromic primes, palindromic perfect powers, and palindromes in other number bases.... Stay tuned for next math lesson (after a brief snack break) when we'll dive deeper into "hyperelevens" and see their connections to the largest prime numbers ever discovered!
------
Combo Class, taught by Domotro, is an unconventional learning experience where anybody (whether they're a fan of normal school or not) can become excited to learn rare things about math, science, language, and more. Also check out the shorter videos on the Combo Class Shorts channel (or TikTok page). Thanks for coming to Combo Class!
DISCLAIMER: The burning clock in the intro (and any other uses of fire, tools, or science experiments in this series) was done in a professional and safe way. Don't try to copy anything you see in this series yourself.

[@eleanorblake697]

I like your explanation of why 11 is the only prime palindrome with an even number of digits. Hope your channel keeps growing!

[@mjohnson2807]

Yeah had a mind explosion moment there 🤯. Really cool

[@noahhorowitz2506]

As someone studying to be a math teacher, I love your pedagogy. Pure enthusiasm for mathematics.

[@Ravenishish]

So fun fact, if you flip the word palindromes you get semordinlap which is a word that describes words and phrases that make other words and phrases when reversed. Like the word Star is Rats backwards. Or Diva and Avid. The other word for that which I know is Heteropalindromes.

[@asheep7797]

Desserts

[@haticeozdemir7917]

Semordnilpaoreteh

[@haticeozdemir7917]

​@a sheep

[@Creeperpro225]

dog=god😊

[@sarthakgupta1853]

Came here from the bonus channel and have to say that I loved the vid

[@NiranjanBharadwaj]

I have to say. Your channel is really underrated. I hope it grows.

[@NoOffenseAnimation]

5:24 I noticed that the n^2, n^3 and n^4 of 11 are all rows in Pascal's triangle, n^5 breaks the very short pattern

[@karlpoppins]

I thought the very same thing! If it is true that these "hollow elevens" form Pascal's triangles when raised to an mth power then it makes sense that at m>4 we stop getting palindromes, since two-digit numbers start creeping in. In fact I'm fairly certain I saw 10s on the m=5 case.

[@wyboo2019]

n^5 only kind of breaks the pattern. if you expand 11^5=(10+1)^5 you get: 11^5=10^5+5*10^4+10*10^3+10*10^2+5*10^1+1*10^0 which is the fifth row of Pascal's Triangle. the problem arises with the fact that we're working in base 10, which only has single-digit representations of numbers up to 9 the reason 11^n gives the nth row of pascal's triangle is due to the nth row and kth element of pascal's triangle is nCk, the binomial coefficient "n choose k," and by the binomial theorem: 11^n=(10+1)^n=nC0*10^n*1^0+nC1*10^(n-1)*1^1+nC2*10^(n-2)*1^2+... and notice that 1^k=1 for all integers k, so it just ends up being: 11^n=(nC0)10^n+(nC1)10^(n-1)+(nC2)10^(n-2)+... which is clearly just the 'decimal expansion' of the nth row of Pascal's Triangle, assuming nCk

[@thatssokwekwe]

I’m guessing the hollowelevens not being palindromes from the fifth power onward is likely because the coefficients of the binomial expansion of (10^k + 1)^n are from the respective row in Pascal’s triangle, and starting at the 5th row you get coefficients greater than 9, which ruins the symmetry? So that’s why, for example, the 1 in the middle of the entries in of the n=5 column is “off”, because that 1 comes from the 10 coefficient in the 5th row of Pascal’s triangle?

[@tobiasgorgen7592]

Happy to have found you! Your energy combined with the fact density in this video is definitly something to behold!!!

[@extrasauceontop]

This has to be my favorite new channel. Please keep uploading. I've binged about everything now

[@gabrielchavez173]

I'm glad the youtube algorithm brought me to this channel! Maybe in the future you could include any references you used in the description for further reading? I feel like busting some paper out and trying to prove the 196 problem, it's so interesting!

[@alc202]

"rats live on no evil star" is a good palindrome sentence

[@Lugmillord]

I just subscribed like 30 minutes ago and your sub count has increased from 1580 to 1610 in that time. Your tetration video is a banger indeed. I wish you good fortune for the future. :) Your energy is amazing! Edit: wow, 1 day later and you are at 3670 subs. Onto a bright future ;)

[@idiom104]

I am rooting for base 11. Hyper-elevans could make a great turning point for large numbers. And mod 7.

[@luna010]

Do the things about all bases (like strictly non-palindromic numbers) also include non-integer, negative, or complex bases?

[@ComboClass]

I just meant the more typical types of bases (integer numbers of base, 2 or greater) but good question, some of the properties might apply to other forms of base too

[@MeriaDuck]

Your whiteboard writing is so neat, you could make a font out of it!

[@emilyrln]

The sparkler as a pointer is on point 😂

[@13donstalos]

This is a criminally under subbed channel. Keep up the great work dude!

[@Rich3rd]

It's so interesting to hear there are computers that can handle math at a billion digits in length. I wonder if they hit a computing threshold or if the number of digits is still growing.

[@ComboClass]

Yeah it's interesting. As we get better algorithms and computers (and sometimes just waiting a long time for a computer to keep running a program) we can test larger and larger ranges for counterexamples of stuff, although to fully know about a family of numbers we usually need a proof more than a computation

[@richardgratton7557]

Love your KZbin handle…wish I’d thought of it!😮

[@landsgevaer]

Integers in the programming language python can grow to arbitrary size (until computer memory becomes the problem)...

[@MeriaDuck]

12:30 A variant of being divisible by eleven is used in many places, called the 'eleven-test' in Dutch / check digit in English. Eleven in many bases is quite interesting I guess. (edited to self-correct for me thinking the check digit is the same as divisibility by eleven) 16:00 / the 196 case: That's just awesome and a side of mathematics I always love: there are problems you can explain quite easily and still we do not know the answer to.

[@vj.xoxoxo]

It's cool to learn and enjoy at the same time! ♥

[@urooshaadnan9794]

next level explanation man

[@zaitzerzazza2830]

Amazing video!!!! Looking forward to the next one😁

[@S.G.Wallner]

Palindromes in the wild are some of my favorite moments. Especially the odometer. I end up getting caught up in the gaps between palindromes.

[@Gunbudder]

2:15 my favorite palindrome is still: a man; a plan; a canal; panama.

[@gheffz]

Love your channel, mate. You are quite the entertainer as well as the message. How's the hips eight months later?

[@somedooby]

Amazing video as always

[@hughe29]

I love your shear competence in your subject. So good to watchl.

[@madeofcake6972]

Hi combo class. I love this channel, great for my brain. :)

[@ww4830]

This video was awesome!

[@justathought88]

". . . secretly palindromic . . ." Neat turn of phrase, my man.

[@Fred-tz7hs]

I want the reversed version for the full palindromic experience. This video is as incomplete as the word "palindromic" isn't even palindromic

[@david-melekh-ysroel]

According to a friend, the 4th power of a number n is called Tesseract

[@4thalt]

Makes sense

[@richardgratton7557]

We should all re-watch this on November 22…😇

[@imprincesswolfy2565]

8:28 123 in base 12 is a palindrome in base 10 (171) I love it

[@to2podemosaprender630]

In spanish is capicua meaning head and tail..

[@marcosluna8127]

No it’s not, it’s palindromo

[@vyliad]

Of the first 68 hollow elevens (including 11): - Most are divisible by another hollow eleven or 17 - None of them are prime except 11 and 101 - There are some other fascinating patterns when you factor the hollow elevens, like how a surprising amount of them include a factor like 9090909091

[@vyliad]

In fact, all of the hollow elevens with an even number of digits seem to be a number like 9090909091 • 11

[@4thalt]

Fun fact: the name for the fear of palindromes is aibohphobia, which is a palindrome

[@deuterium_oxide7382]

fun fact: while the word palindrome isn't a palindrome, the name for the fear of palindromes (aibohphobia) is

[@chrisg3030]

What about partial palindromes, that is a number containing a palindromic sequence of digits even if the whole thing isn't a palindrome? One reason why that could be interesting is that for any even number base, beginning with decimal, the number consisting of all the digits running consecutively from 1 to the top single digit, and the reverse, when divided by that digit seems to contain a palindromic sequence of at least 3 terms. For example in decimal 123456789/9 = 13717421, 987654321/9 = 109739369, containing 717 and 393 respectively. In base12 the corresponding palindromic sequences are B4B and 181, base 14 has B292B and 3C5C3.

[@KingLarbear]

You're going to be the reason why I can't sleep tonight lol

[@jayvaghela9888]

Why this channel is amazing without having any animations or graphs ?

[@justathought88]

It's all his fault!

[@to2podemosaprender630]

I love symmetry... maybe because I'm not so symmetrical... 😃😄😀😁

[@bagelnine9]

(11:00) Fun fact: I once saw the number 103 in a dream. It was the age rating of a movie that my parents were watching on Netflix.

[@kierafrost2550]

I watched this video and saw your comment just 2-3 hours ago. I am now checking a show I might want to see, and it says it’s free for people under 13 and… over 103. What a coincidence, it’s such an oddly specific age limit!

[@Sugar3Glider]

Base 20 sounds like it would be a great system to use

[@wankachalawea]

6:25 up to n to the forth the pattern seems like pascal's triangle

[@ofconsciousness]

So cool!

[@MateoAcosta-zi2us]

wow!! you are fucking awesome! Your knowledge, your playfulness, your energy, I hope you the best! and thank you very much hehe!

[@idiom104]

Sorry but question. If it were possible let j=any variable a/0=x j(a/0)=jx ja/j0=jx You can never multiply any number(j) by (a/0) and also change the zero underneath the divisor to any other number(k). I conjucture that if we can manipulate the zero under the devisor into k allowing that k cannot equal zero, the following statement can be solved. a/0=x

[@cv21a]

Thanks

[@vaheakli4551]

ok, fyi, my favourite palindrome is "оголи жопу пожилого" which translates as "undress ass of aged human"

[@KingLarbear]

37 and 73 have a crazy relationship

[@sscutoid]

5:41 pascal's triangle????

[@Very.Crazy.Math.Pistols]

196 is 14². And 14 Is 2*7. Coincidence ? 🤔. Nice work haha, cool channel : - )

[@eliaswilliams971]

I do my work in base 10

[@santerisatama5409]

In Finnish self-test is, drum rolll...: 'itsetesti'.

[@finlordlegendarygamer7014]

Let's make that like button palindromic! It's 419 rn.

[@stillme4084]

Sister primes cousin prime. I love primes

[@truejeffanderson]

11² is palindrome and all the zeros you can fit between. 101,1001,10001,100001. Then I think there might be some powers of these that work. Maybe 1001³ is palindrome? * On purpose: didn't check on paper, calculator or watch all of video. Mental guessing from 3 minutes in

[@GeometryDasherGionic]

12^2=144 and swap the digits 441=21^2

[@jaredellison326]

My favorite palindrome: lonely tylenol

[@sallylauper8222]

I can has complex palindrome?

[@takeguess]

Will you please standardize all symbols in mathematics? I would pay for a book on that for sure.

[@TheMathPlaygroundMathJoy]

17 is a palindrome in base one-and-a-half 😎

[@pingnick]

♾

[@gametalk3149]

11+020=31 which isn’t a palindrome

[@stillme4084]

I LOVE PRIMES

[@maximilianarold]

Clicked on the video at 14:41 o clock. Do I get a prize?

[@toanpham4110]

✅

[@Madoc_EU]

Every number is a palindrome in base 1.

[@ToanPham-wr7xe]

😮

[@lloydgush]

Where the F'ing F you get all these clocks?

[@JamieJamez]

You can donate old clocks to him

[@Rich3rd]

😄😄

[@maht0x]

step on no pets

[@Gamerguld]

People with abihophobia watching this...

[@_skyyskater]

May your subscriber count be tetrated!

[@nathanielkilmer5022]

They're only palindromic because you're too lazy to write the leading zeros.

[@jamesgarzo6967]

Bruh I had to pause at palinilap lmfao

[@jaredellison326]

Love this comment

[@stickmcskunky4345]

11:71 tnemoM skaeP niwT