@Mr.Xcoder Normally I would say yes, but since these sequences are infinite in both directions, I have to hesitantly say no. (If you offer a compelling argument I could easily change my mind on this) If you can find a way to print in both directions that would be fine.

@Steadybox Sure that sounds fine. Probably not the easiest way to do it though.

@Zgarb Sorry I made another mistake in the equation TFeld is right it should be minus. I must be off it today or something...

@xnor It means that given the subsection you can use the property to derive all the other members of the sequence, for example if you know 2,2,1 is in the sequence you can find every other member. Basically it means that it is a subsection that only exists in one sequence with the property.

I also think "uniquely determines the sequence" is a bit confusing, even after your explanation. How about outputting a subsection that can be repeated indefinitely both ways to construct the actual sequence? Like the repetend of a rational number.

@aditsu I choose the definition there very carefully, it's a little more lenient in someways and stricter than others than the definition you suggest. I would like to make it as clear as possible but that is the idea I want to use.

Except we don't really understand what it means... Btw, is my idea acceptable as an output choice? In fact.. the additional input thing might end up being easier.

@aditsu No your idea is not sufficient, for example 2,2 when repeated infinitely makes a valid sequence but it could also be a part of ... 2,2,1,2,2,1,2,2,1 ... thus it doesn't uniquely determine a sequence.

2,2 uniquely determines the …2,2,2,2… sequence (1-juggler) and does NOT determine the …2,2,1,2,2,1… sequence (2-juggler).

@aditsu 2,2 does not uniquely determine any sequence, its part of both of the sequences.

Yes it does: repeat 2,2 once → 2,2,2,2, repeat again → 2,2,2,2,2,2, etc. There's absolutely no way to get a 1 from repeating 2,2. The sequence you get is always unique.

The problem with 2,2 is that if you try to calculate the next term it will attempt to reference the term before the begining of the sequence

you know it must be of the form x,2,2,x but you don't have enough information to deduce x

I'm not calculating anything, I'm repeating the output indefinitely

Yes but that will skip over possible resolutions for example 2,2,1,2,2,1,2,2,1,2,2,1,2,2

2,2 would not be a valid output for that sequence, however, 2,2,1 would be valid

what part of "repeating" is unclear?

May we assume n ≥ 2?

@Mr.Xcoder Oh yeah sure, I'll add them

@aditsu I think we are having two different discussions.

I'm saying that 2,2 does not uniquely determine a sequence, however it when repeated does form a sequence

of course I'm talking about repeating it indefinitely, that's the only thing I've been talking about in all my comments

I was trying to demonstrate that the two are different

@WheatWizard what I can't understand is how you determine a(n) to begin with

@EriktheOutgolfer You look at the term before it a(n-1) then look at the term that many before that a(n-1-a(n-1)) that is the result

but it's infinite on both sides

so for example how do we define a(0) to begin with

it's periodic though

Lets say you have ` ... 2,2,1`

You know that the term 3 before the 1 must also be a 2 because the 1 is after a 2, and must have come from somewhere

now you have ... 1,2,2,1

huh

now I'm more confused

But the first 2 must have come from somewhere, inparticular right before the 1

so you have ... 2,1,2,2,1

@EriktheOutgolfer Err... What are you confused on?

Do you understand how we can build terms of the sequence forward?

@WheatWizard how do we define such a sequence at all, what's the "initial element(s)"?

We are defining a class of sequences, not a particular sequence

The question is: Once I fill in a few terms what must the rest of the sequence look like

@Mr.Xcoder I think so, seems like it would work

@Mr.Xcoder that's kinda what I did :)

Thank you!

@EriktheOutgolfer Ok I have to go. sorry I can't explain it more

alright then

@WheatWizard for the record, you haven't answered my initial question, but it's somewhat moot now

What was that?

would it be ok to output a subsection that defines the sequence by in[de]finite repetition?

Not unless that subsection is only a subsection of one such sequence.

I don't understand what you're saying..

there's only one way to repeat a section

@EriktheOutgolfer it's a periodic/cyclical sequence, it doesn't really start from any particular point, but once you define it (e.g. by the repeating part, which Wheat Wizard can't seem to agree with), you can verify whether it satisfies the property

Yay I am glad it works :)

@aditsu Yes but it does not uniquely determine a sequence.

The 2,2 example still holds, it is a subsection of 2,2,2,2,2,2,2,2 and 2,2,1,2,2,1,2,2,1,2,2,1,2,2,1

repetition always uniquely determines a unique sequence

@WheatWizard So? aditsu's argument aside, only one of those sequences satisfies the property of being a 1-juggler.

@aditsu You are throwing around the phrase "uniquely determine" in a context where it doesn't make sense.

@PeterTaylor Yes, one is a 1 juggler and the other is a 2 juggler

we're talking about determining the sequence, how does it not make sense?

@aditsu Because while it is true that if you include the function that maps it to the sequence it "determines" the sequence, it doesn't determine the sequence on its own. Just like filling in part of the sudoku grid might determine the entire grid, filling in a subsequence might determine the entire sequence.

@WheatWizard ok, so what you're saying is that you STILL don't understand the meaning of repetition

I understand what you mean by repition

I don't think you understand what the phrase "uniquely determine" means

ok, tell me how you get from 2,2 to 2,2,1,2,2,1,2,2,1,2,2,1,2,2,1 BY REPETITION

You don't

uniquely determine means given the subsequence there is only one way to make a sequence that contains it

then the sequence 2,2,2,2,2,2,2,2 is unique

but 2,2 does not determine it, there is not enough information in 2,2 to know what it is a subsequence of

I said BY REPETITION

I understand

> would it be ok to output a subsection that defines the sequence by in[de]finite repetition?

repition is different from unique determination that is my claim

repetition generates a (unique) infinite sequence

therefore it determines a sequence

I think I'm done

we are going in circles here

obviously..

anyway, by this point I think I'm starting to understand what you initially meant by "output a continuous subsection of the sequence that, with the given property uniquely determines the sequence" although you never really explained it

you're talking about using the a(n+1)=a(n-a(n)) property to identify other terms of the sequence (right?), although you can only go back that way; I suppose going forward would be based on the.. wait for it... repetition

I was suggesting using repetition alone to build the sequence from the outputted section, but you refuse to even understand the concept