Yeah, I'm fully aware of what merged sequences are. So a sequence that simply merges with another is a sister sequence. Correct? If so, why 2 different terms for the same thing? Isn't it just a merged sequence?

This brings up another question: I see multiple merges for many of the merged sequences shown as such on your pages. How do you decide which sequence to use for the merge? I would think that it should be the lowest sequence that it merges with but I see that sometimes it is and sometimes it isn't. It doesn't appear consistent to me. What is the rule for deciding which sequence that another merges with when there are multiple merges?


Gary

[quote=gd_barnes;180270]Yeah, I'm fully aware of what merged sequences are. So a sequence that simply merges with another is a sister sequence. Correct? If so, why 2 different terms for the same thing? Isn't it just a merged sequence?[/quote]
No. As far as I know, I made up the "sister sequence" terminology, and it is separate from a merged sequence. Merged sequences are where n1.i1=n2.i2, (note: I'm using n.i to mean the [I]i[/I]th iteration of sequence [I]n[/I]) sister sequences are where (n1.i1)/(driver1)=(n2.i2)/(driver2) for many subsequent lines (not just a one-time coincidence or something).
[quote=gd_barnes;180270] This brings up another question: I see multiple merges for many of the merged sequences shown as such on your pages. How do you decide which sequence to use for the merge? I would think that it should be the lowest sequence that it merges with but I see that sometimes it is and sometimes it isn't. It doesn't appear consistent to me. What is the rule for deciding which sequence that another merges with when there are multiple merges?


Gary[/quote]
Perhaps the lowest at time of merge? I'd expect it to just be the smallest, but if it's not consistent...I don't really know.

[quote=Mini-Geek;180278]No. As far as I know, I made up the "sister sequence" terminology, and it is separate from a merged sequence. Merged sequences are where n1.i1=n2.i2, (note: I'm using n.i to mean the [I]i[/I]th iteration of sequence [I]n[/I]) sister sequences are where (n1.i1)/(driver1)=(n2.i2)/(driver2) for many subsequent lines (not just a one-time coincidence or something).[/quote]

Hum. That is not what Karsten implied at all. He was describing a sequence that directly merged with another, i.e. that they encounter the same value at some point.

Let me give an example and see if I have the sister sequence definition straight. (I learn better by examples).

If sequence x has a value of 2000000004 at some index and sequence y has a value of 1000000002 at some index, i.e. 2000000004/2, then they may run "in sync" for many indexes and so are considered sister sequences. And further...they may run in sync for a while and then become out of sync after an extended period of time.

Is that correct? If so, it is completely different than what Karsten stated, which only referred to what I understand as merged sequences.

Oh boy, I just this second realized that I referenced "sister" sequence in my follow up. I has asked about "side" sequences originally...probably 2 different things.

OK, if my "sister" sequence definition is correct above, is Karsten's explanation of a "side" sequence correct? If so, my question is: Why are there 2 different names for the same thing: That is a "merged" sequence and a "side" sequence.

Sorry for the confusion.


Gary

"Merges" are where a value from one sequence is equal to a value from another, [U]lower[/U] sequence (e.g. 314718 merges with 4788).

"Side-sequences" are where a value from one sequence is equal to a value from another, [U]higher[/U] sequence (e.g. 56440 is a side-sequence of 1578).

Ah, very good. Thanks for the explanation on side sequences.

Can someone confirm that my understanding of "sister" sequences is correct?

Mini-Geek gave an example in his first post of the Sister-thread:

24384 and 100651008 are 'sisters' (in his notation/definiton), because the both begin with <driver>*3:
24384 -> driver = 2^6*127
100651008 -> driver = 2^12*8191

both sequences run 'together' with their own driver and the [b]same[/b] remaining part of each index. the numbers for same indices are different so they are not sideseqs at all.

[quote=10metreh;180293]"Merges" are where a value from one sequence is equal to a value from another, [U]lower[/U] sequence (e.g. 314718 merges with 4788).

"Side-sequences" are where a value from one sequence is equal to a value from another, [U]higher[/U] sequence (e.g. 56440 is a side-sequence of 1578).[/quote]
So are all of these statements equivalent with x>y, or not?
x merges with y
x is a side-sequence of y
y has a side-sequence of x

Does the order of computing have anything to do with it? 56440 and 1578 merge to have the same number, so why does the DB not say that one merges into the other? Is it because there is in fact a difference between a merge and a side sequence? I'm not seeing the difference.

[quote=Mini-Geek;180329]So are all of these statements equivalent with x>y, or not?
x merges with y
x is a side-sequence of y
y has a side-sequence of x

Does the order of computing have anything to do with it? 56440 and 1578 merge to have the same number, so why does the DB not say that one merges into the other? Is it because there is in fact a difference between a merge and a side sequence? I'm not seeing the difference.[/quote]

There is a difference. Merges are when the sequence drops below its starting number and joins another sequence (eg 314718 drops down to 5 digits after a peak of about 90, where it merges with 4788). With side-sequences, the sequence does not drop below its starting value, so 1578, which only drops to 56440, acquires 56440 as a side-sequence.

[quote=10metreh;180337]There is a difference. Merges are when the sequence drops below its starting number and joins another sequence (eg 314718 drops down to 5 digits after a peak of about 90, where it merges with 4788). With side-sequences, the sequence does not drop below its starting value, so 1578, which only drops to 56440, acquires 56440 as a side-sequence.[/quote]
Oh, I get it now. :smile: So merges are where a sequence's value drops below its starting value, so n1.i1=n2=n2.0 with n2<n1, whereas side sequences are n1.i1=n2.i2 with i1,i2>0.

Actually, I wouldn't count 56440 as a side sequence - it is part of 1578's sequence and not a side sequence at all.

I usually think of side sequences to be when x->...z and y->...z where z is bigger than both.

For example, 64116:19 = 10284:354 = 15752044

DB calls this a merge however.

When two sequences are shown to have a common element, from that point onwards, only one needs to be computed (it is a deterministic computation, after all). The sequences can be said to have "merged" or had a "confluence". One of them (the one with lower starting point) will be designated the main sequence, and the other will be designated a side-sequence.