20201001, 13:43  #1 
Nov 2016
2^{2}·3·211 Posts 
836
836 is the secondsmallest weird number.
836 is the smallest weird number divisible by 4. 836 is the smallest weird number which is also untouchable number. The square of 836 (698896) is the smallest palindromic number with an even number of digits (there are no 2digit palindromic numbers not 4digit palindromic numbers) (all evendigit palindromic numbers are divisible by 11, thus these numbers must be divisible by 11^2 = 121), and this number can be rotated to another palindromic number 968869. 836 is the Sierpinski base < 1024 which has the 3rd largest exponent of k=7 (the first and second largest exponent bases are 1004 and 398, respectively) 836 is the smallest even n such that n/2 is not prime power binomial(n,n/2) == 2 (mod n/2) (by Wolstenholme's theorem, this equation is true if n/2 is prime, prime square, or prime cube (except 8 and 27), all other known such even n are == 2 mod 4 (i.e. n/2 is odd), an open problem is whether 836 is the only such even n divisible by 4 (i.e. n/2 is even)? 
20201001, 17:10  #2  
Jun 2015
Vallejo, CA/.
2^{3}·11^{2} Posts 
Quote:
isn't it that 22, 33, 44... 99 are 2digit palindromic numbers? And what about 1001, 1111, 1221, 1331... 9889, 9999. Aren't those 4 digit palindromic numbers? 

20201001, 19:17  #3  
Feb 2017
Nowhere
3888_{10} Posts 
Quote:


20201002, 04:38  #4 
Nov 2016
2^{2}·3·211 Posts 

20201002, 06:44  #5 
Romulan Interpreter
Jun 2011
Thailand
2×4,481 Posts 
Yep, she means squares.
OTOH, 83^2=6889 is a nice palindromic square. Don't believe? Write it down on a paper, rotate the paper 180 degrees, and you will see it is the same! 
20201002, 10:02  #6  
Nov 2016
2^{2}·3·211 Posts 
Quote:


20201002, 10:03  #7 
Nov 2016
2^{2}×3×211 Posts 

20201002, 11:51  #8 
Romulan Interpreter
Jun 2011
Thailand
2×4,481 Posts 

20201002, 12:18  #9 
Nov 2016
100111100100_{2} Posts 
This is my favorite champion in League of Legends: Janna (though I usually play Ahri, Thresh, and Xayah.
Last fiddled with by sweety439 on 20201002 at 12:20 
20201003, 15:36  #10 
6809 > 6502
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Aug 2003
101×103 Posts
2^{3}×1,117 Posts 
Remember avatars don't always look like the individual behind the keyboard (like yours).
https://en.wikipedia.org/wiki/On_the...you%27re_a_dog 
20201003, 16:03  #11 
Romulan Interpreter
Jun 2011
Thailand
2·4,481 Posts 
What? Do you mean you, and Dr. S, and all other people here, are lying in your avatars, and I am the only honest guy here? Geeezzz.. I won't talk to you anymore, and I will change my avatar to not look like me anymore!
