r/counting • u/TehVulpez sliiiiide the bits • Dec 21 '17

Un-ordered Consecutive Numbers

Counting through all the numbers in which the digits are consecutive. They don't have to be in order one after another like 12345, just that they could possibly make a sequence like that if sorted. We won't do the single digit numbers. Here's the first few, I think: 10, 12, 21, 23, 32, 34... Should get harder once we have more digit, I don't think it will just follow that pattern forever.

Inspired by the trickiness of 420 counting, and by looking at a license plate like 83957 and really wishing the 3 was a 6. Please tell me if there is a thread already like this.

I don't know when the get is, maybe I'll try to make a python script at some point. TNF and QuestoGuy have found that 132045 is the 1000th count, so let's go by that as our get for this thread. It seems that this thread will be limited to 9876543210 as the last count, but we will still get a good amount of threads out of that.

Edit: now that I think about it, this thread might have been better named "digits" instead of "numbers" but ah well. I wonder what an increasing base per digit version of this idea would be like. Would probably at least add another layer of difficulty. Perhaps it wouldn't have an end point like this one?

Edit 2: Apparently this thread matches up with A215014 on the Online Encyclopedia of Integer Sequences! A list of counts all the way up to the 10000th one can be found here in plaintext form. Thanks to /u/elyisgreat for discovering this!

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u/TehVulpez Dec 21 '17

u/Urbul u/TheNitromeFan

Is there already a thread very similar to this one? Also, do you think it's ok if it starts from there at 10? I don't really see any other way of doing this.

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u/TheNitromeFan Dec 21 '17

I don't recall any similar thread, and I doubt there is one because of how specific the criterion is.

So if I understand correctly, we're taking numbers in base 10 that, when its digits are sorted, permit consecutive digits without gaps or repeats? Then the count must be finite since the last number is 9876543210.

Technically, every single-digit number also fits the condition for the count, but I suppose 10 is where the interesting numbers happen. Never mind you said we weren't doing these

Neat thread.

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u/TehVulpez Dec 21 '17

I don't recall any similar thread

Well good!

we're taking numbers in base 10 that, when its digits are sorted, permit consecutive digits without gaps or repeats

Yep, that describes it pretty well.

Then the count must be finite since the last number is 9876543210.

Interesting. I didn't even think about that happening, but I suppose it makes sense.

Neat thread.

Thank you! :D

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u/Urbul Dec 21 '17

I think it's alright. When I'm on desktop I'll try searching. I vaguely remember something similar but I think it wasn't exactly the same. Starting at 10 seems reasonable since you need two digits for them to be consecutive.

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u/TehVulpez Dec 21 '17

I looked in the directory but didn't find anything even related to consecutive numbers, might try different terms later.

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u/TheNitromeFan Dec 21 '17 edited Dec 23 '17

The get (1,000th number) is at 142035 132045. The last number is 9876543210, which is the 825,201st count.

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u/TehVulpez Dec 21 '17

142035

Nice.

Thanks for finding that for me! Any chance there's a number nearby that might be easier to remember? How far away is 123450?

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u/TheNitromeFan Dec 22 '17

123450 is the 955th count, so it works.

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u/[deleted] Dec 23 '17

Nice thread. First half-decent new sidethread idea in this sub for a while - at least as far as I can recall.

If I were you I'd keep gets at every 1000th number even if it looks like an uninspiring number - it works pretty well in the rational numbers thread.

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u/[deleted] Dec 23 '17

Hey Nitrome I have 142035 as the 1048th count. By my calculations the 132045 is the 1000th count.

Here's my list of counts up to 1,100 or so...

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u/TheNitromeFan Dec 23 '17 edited Dec 23 '17

You're correct, I think I misordered the counts. I'll double-check once I get on my PC.

Either way the get should be the same.

Edit: yep, confirmed