@riggedtoexplode Yeah. Algorithms are not necessarily opposed to this, either. If you could turn them on or off, tweak their parameters, and see how they work, I think it would be more like exploring.

But sometimes I do wish that finding people on the fediverse was easier, lol

re: math 

@olamundo@qoto.org One relatively simple observation is that every number in any sequence mod 5 is always 0 or 4, except for the first number of the sequence (which can be anything of course).

Something else I noticed is a mysterious symmetry. If you look at all the numbers between 1 and 3^4 which run for exactly 4 steps, you get these numbers:

[11, 14, 29, 32, 43, 46, 61, 64]

They are symmetrical around 37.5. That is, 11 and 64 are equidistant to 37.5, 14 and 61 are also equidistant to 37.5, and so on.

And this is also true for sequences of length 5 between 1 and 3^5, which are symmetrical around 118.5. And so on, up to sequences of length 15 between 1 and 3^15, which are symmetrical around 7174450.5. That's as far as I've checked via computer, but I suspect that it keeps on being true for lengths greater than that, too.

Anyway, thanks for interacting!

re: math 

@olamundo@qoto.org Sorry, the description I gave leaves a lot implicit. I actually copied it straight from the blog post, and maybe it was more clear in the blog post. But yes, 3k is any multiple of 3, and r is either 1 or 2.

So 1 would have k=0 and r=1, 2 would have k=0 and r=2, 4 would have k=1 and r=1, 5 would have k=1 and r=2, etc.

These are the first 10 sequences, if that helps:

1: [1, 4, 9]

2: [2, 5, 10, 19, 34, 59, 100, 169, 284, 475, 794, 1325, 2210, 3685, 6144]

3: [3]

4: [4, 9]

5: [5, 10, 19, 34, 59, 100, 169, 284, 475, 794, 1325, 2210, 3685, 6144]

6: [6]

7: [7, 14, 25, 44, 75]

8: [8, 15]

9: [9]

10: [10, 19, 34, 59, 100, 169, 284, 475, 794, 1325, 2210, 3685, 6144]

KDE is pretty nice, it's my desktop environment of choice. It's kind of interesting that it's considered "trending" by this instance right now lol.

math 

I stumbled on this collatz-like open problem recently, and was nerd-sniped into spending a lot of time thinking about. The problem is this: given the following function L, does it terminate on all inputs?

L(3k) = 0
L(3k + r) = L(5k + r + 3)

Note that it's an open problem, so finding a solution is not very likely.

(source for the problem:)
nickdrozd.github.io/2021/09/25

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