Content pfp
Content
@
0 reply
0 recast
0 reaction

Scott Kominers pfp
Scott Kominers
@skominers
Thanksgiving this year falls on the 28th, and 28 is a perfect number – meaning that it is equal to the sum of its proper divisors (28 = 1 + 2 + 4 + 7 + 14). So... I hope you have a truly perfect Thanksgiving!! (The preceding perfect number is 6 and the next is 496 (followed by 8128), which means that the 28th is the only candidate for a "perfect Thanksgiving," at least in the Gregorian calendar.)
1 reply
5 recasts
15 reactions

Scott Kominers pfp
Scott Kominers
@skominers
Also, today's date in the form "112824" is the number of fixed proper tree polycubes made up of seven four-dimensional cubes (see https://link.springer.com/chapter/10.1007/978-3-642-21204-8_13 for more information). And 112824 = (3 + 4)^6 - (3^6 + 4^6).
1 reply
0 recast
4 reactions

Scott Kominers pfp
Scott Kominers
@skominers
If you instead write today's date in the form "241128," you get a generalized Stirling number. And while it's unclear whether there is a reason to write the date as "112428," that does happen to be the number of self-inverse permutations of {1,...,12} with element displacement restricted to at most 9.
1 reply
0 recast
3 reactions

Scott Kominers pfp
Scott Kominers
@skominers
Meanwhile, 1128 is triangular, hexagonal, icosahedral(!), and the smallest positive integer that is a multiple of both 8 and 12 and has both an 8 and a 12 in its decimal representation (the next such integer is 1248, followed by 4128, 7128, and 8112).
1 reply
0 recast
3 reactions

Scott Kominers pfp
Scott Kominers
@skominers
And finally, 1128 and 2024 are both positions of new primes in the sequence that starts with 1,1 and then successively enumerates the minimal positive integers such that all of the adjacent pair products in the sequence are distinct. Delicious, QED!
0 reply
0 recast
3 reactions