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 2020-10-01, 13:43 #1 sweety439     Nov 2016 22·3·211 Posts 836 836 is the second-smallest 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 2-digit palindromic numbers not 4-digit palindromic numbers) (all even-digit 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 3-rd 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)?
2020-10-01, 17:10   #2
rudy235

Jun 2015
Vallejo, CA/.

23·112 Posts

Quote:
 Originally Posted by sweety439 836 is the second-smallest weird number. (there are no 2-digit palindromic numbers not 4-digit palindromic numbers) (all even-digit 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. [/B]
Forgive me if i'm wrong.

isn't it that 22, 33, 44... 99 are 2-digit palindromic numbers?

And what about 1001, 1111, 1221, 1331... 9889, 9999. Aren't those 4 digit palindromic numbers?

2020-10-01, 19:17   #3
Dr Sardonicus

Feb 2017
Nowhere

388810 Posts

Quote:
 Originally Posted by sweety439 The square of 836 (698896) is the smallest palindromic number with an even number of digits (there are no 2-digit palindromic numbers not 4-digit palindromic numbers) (all even-digit 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.
Do you mean palindromic squares?

2020-10-02, 04:38   #4
sweety439

Nov 2016

22·3·211 Posts

Quote:
 Originally Posted by Dr Sardonicus Do you mean palindromic squares?
Yes, my typo, I mean palindromic squares.

 2020-10-02, 06:44 #5 LaurV 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!
2020-10-02, 10:02   #6
sweety439

Nov 2016

22·3·211 Posts

Quote:
 Originally Posted by LaurV 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!
6889 is not palindromic

2020-10-02, 10:03   #7
sweety439

Nov 2016

22×3×211 Posts

Quote:
 Originally Posted by LaurV 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!
"she"?? WTF!!!

2020-10-02, 11:51   #8
LaurV
Romulan Interpreter

Jun 2011
Thailand

2×4,481 Posts

Quote:
 Originally Posted by sweety439 "she"?? WTF!!!

2020-10-02, 12:18   #9
sweety439

Nov 2016

1001111001002 Posts

Quote:
 Originally Posted by LaurV Well... from your avatar(s)...
This is my favorite champion in League of Legends: Janna (though I usually play Ahri, Thresh, and Xayah.

Last fiddled with by sweety439 on 2020-10-02 at 12:20

2020-10-03, 15:36   #10
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

23×1,117 Posts

Quote:
 Originally Posted by LaurV Well... from your avatar(s)...
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

 2020-10-03, 16:03 #11 LaurV 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!