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Old 2020-10-01, 13:43   #1
sweety439
 
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Default 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)?
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Old 2020-10-01, 17:10   #2
rudy235
 
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Quote:
Originally Posted by sweety439 View Post
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?
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Old 2020-10-01, 19:17   #3
Dr Sardonicus
 
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Quote:
Originally Posted by sweety439 View Post
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?
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Old 2020-10-02, 04:38   #4
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Originally Posted by Dr Sardonicus View Post
Do you mean palindromic squares?
Yes, my typo, I mean palindromic squares.
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Old 2020-10-02, 06:44   #5
LaurV
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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!
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Old 2020-10-02, 10:02   #6
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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
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Old 2020-10-02, 10:03   #7
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Originally Posted by LaurV View Post
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!!!
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Old 2020-10-02, 11:51   #8
LaurV
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Quote:
Originally Posted by sweety439 View Post
"she"?? WTF!!!
Well... from your avatar(s)...
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Old 2020-10-02, 12:18   #9
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Quote:
Originally Posted by LaurV View Post
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
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Old 2020-10-03, 15:36   #10
Uncwilly
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Quote:
Originally Posted by LaurV View Post
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
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Old 2020-10-03, 16:03   #11
LaurV
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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!
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