Fun math facts about 2023

18gjm

-9razi

9Zach Stein-Perlman

2Throwaway2367

3Zach Stein-Perlman

1[anonymous]

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(These are stolen from @joshuacooper@mathstodon.xyz, who found them by looking for 2023 in OEIS.)

It's the number of tilings of a 4×4 square with right triominoes and 1×1 tiles.

It's the sum over all 4-tuples (a,b,c,d) of divisors of 18 of the quantity gcd(a,b,c,d).

It's the number of connected (unlabeled) graphs on 9 vertices that occur as induced subgraphs of a Hamming graph (=Cartesian product of paths).

(A few more from my own OEIS-mining.)

2023 = 45^2 - 2. (Not very exciting, but surely no worse than 2^11 - 5^2.)

The number n=28322 has the (quite unusual; it's 16th-smallest) property that n^2 is a multiple of the sum of all distinct prime divisors of n^2+1. The quotient is 2023^2.

2023 is the remainder on dividing 7^7 by 7!.

Let A(n) be the average of all primes dividing n. Then 2023 is the second-smallest positive integer n for which A(n) and A(n+1) are equal. (The smallest is 459.)

2023 = (2+0+2+3)(2^2+0^2+2^2+3^2)^2; 2023 is the smallest number other than 1 for which this happens.

2023=7×172

Maybe that's not fun enough? Try this:

2023=211−52

Or better yet:

20233=31176029+245568392384321573

We can scientifically quantify how fun a math fact is, so we can rest assured that this is the funnest fact about 2023 ever discovered.

But if it's not to your liking:

2023=21034−141

2023=5511+2417

2023=3647+2717

2023=24792−3672=(22797)2−(337)2

Happy New Year!