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 EdH 2011-12-30 05:34

Aliquot genealogy project

Is there a "family tree" of sorts that shows all the merges for sequences under 1M in the db?

 schickel 2011-12-30 06:56

[QUOTE=EdH;284020]Is there a "family tree" of sorts that shows all the merges for sequences under 1M in the db?[/QUOTE]No. The closest thing would be Wolfgang's C30C90 table. If you look in there, you will find a list of open sequences, with the first c9 and first c30 encountered during their lifetime. Some merges and terminations are listed, but at the top it says:[quote=Wolfgang]All numbers you will not find in the following table are key-numbers of side-sequences. Have a look into the matrix of ALIQUOT. You will find them there.[/quote]Last updated 2009, so not real current.

The matrix listed is one that is maintained by a TurboPascal program that is listed in the download section. Said matrix is a listing of sequence starting numbers and a status which is indicated by a number: 0 for open, the prime a sequence terminates at, or the member of an aliquot cycle that a sequence merges with. Not so useful if you want to fiind out what merges with what, from either side, but you could get a count of how many sequences terminate at which prime. Major drawback: uses "1" for the starting line of a sequence file, rather than "0"....another drawback: the record file has not been updated since 1994.

 science_man_88 2011-12-30 12:54

[QUOTE=schickel;284031]No. The closest thing would be Wolfgang's C30C90 table. If you look in there, you will find a list of open sequences, with the first c9 and first c30 encountered during their lifetime. Some merges and terminations are listed, but at the top it says:Last updated 2009, so not real current.

The matrix listed is one that is maintained by a TurboPascal program that is listed in the download section. Said matrix is a listing of sequence starting numbers and a status which is indicated by a number: 0 for open, the prime a sequence terminates at, or the member of an aliquot cycle that a sequence merges with. Not so useful if you want to fiind out what merges with what, from either side, but you could get a count of how many sequences terminate at which prime. Major drawback: uses "1" for the starting line of a sequence file, rather than "0"....another drawback: the record file has not been updated since 1994.[/QUOTE] yeah I could play with my ali and aligen scripts ( they work backwards) again but I doubt anything interesting comes out of it.

 EdH 2011-12-30 14:44

@schickel: Thanks. I looked at the c30c90 file a while ago, but not the other reference, yet. You have posted an "AllSeq.zip" file in the past, so there must be a method to query just the last line from the db for all the sequences. I can get full .elf files, but all my last line attempts end up downloading an .html page. How can I get just the last lines, either individually or all at once (preferred)? For that matter, is there a reference that shows what queries are available for the db?

If I can get all the last lines, I'm pretty sure I can write something that can build a merge listing. Of course, then I need to figure out the best method for displaying merges...

 schickel 2011-12-30 19:59

[QUOTE=EdH;284055]@schickel: Thanks. I looked at the c30c90 file a while ago, but not the other reference, yet. [/quote]Ah, OK. I wasn't sure how much of the background info you were aware of, since it has gotten harder to keep track of who joined when and who knows how much....[quote]You have posted an "AllSeq.zip" file in the past, so there must be a method to query just the last line from the db for all the sequences. I can get full .elf files, but all my last line attempts end up downloading an .html page. [/quote]I use a 5-lb sledgehammer to do the job. I have a list of the open sequences and just download the .elf file for each one.

I don't do the whole range but once a week or so, since it is so query intensive. I keep meaning to sit down and do a "last line" tool Real Soon Now.[quote] How can I get just the last lines, either individually or all at once (preferred)?[/quote]Unfortunately, if you use the "show last element" radio button, the last line is shown as an html page. The last line [B]is[/B] there, but you have to parse it out of the html....[quote]For that matter, is there a reference that shows what queries are available for the db?[/quote]Not really. Some of the queries available were discussed over in the FactorDb thread, but I would say that the only one who knows what all is available is Syd....[quote]If I can get all the last lines, I'm pretty sure I can write something that can build a merge listing. Of course, then I need to figure out the best method for displaying merges...[/QUOTE]I have been thinking along those lines, too. So far it seems to me there is no really easy way to do things, since if you want to make it comprehensive, you almost have to have 1.000.000 entries (less the primes since they're easy), even if most of them are "S[sub]n[/sub] merges with x after y lines" or "S[sub]n[/sub]terminates in x after y lines" with y<10.....

 science_man_88 2011-12-30 20:16

[QUOTE=schickel;284098] even if most of them are "S[sub]n[/sub] merges with x after y lines" or "S[sub]n[/sub]terminates in x after y lines" with y<10.....[/QUOTE]

this good enough for you:

[CODE]aligen5(w,s)=for(z=w,s,for(x=1,#ali(z),print1(ali(z)[x]":i2=");for(y=1,#ali(ali(z)[x]),print1(ali(ali(z)[x])[y]":i3=")));print())[/CODE]

? it was a slight change to my aligen script.

 EdH 2011-12-31 05:08

[QUOTE=schickel;284098]Ah, OK. I wasn't sure how much of the background info you were aware of, since it has gotten harder to keep track of who joined when and who knows how much....[/QUOTE]
Wow, I guess I've been around for two years now, according to my stats... But I should still be considered as someone who doesn't know much.:smile:
[QUOTE=schickel;284098]I use a 5-lb sledgehammer to do the job. I have a list of the open sequences and just download the .elf file for each one.[/QUOTE]
The more I look at this, the larger a task it seems. To download 1M .elfs, or even just last lines, is a huge endeavor, itself. Even If I d/l 1k per day, it would take 3 years to complete...
[QUOTE=schickel;284098]I don't do the whole range but once a week or so, since it is so query intensive. I keep meaning to sit down and do a "last line" tool Real Soon Now.[/QUOTE]
I'm going to have to think a bit more about this. Things like maybe I should eliminate those sequences that end in primes or cycles.

[QUOTE=schickel;284098]Unfortunately, if you use the "show last element" radio button, the last line is shown as an html page. The last line [B]is[/B] there, but you have to parse it out of the html....[/QUOTE]
It would be easier to parse the .elf files, although they would be larger.
[QUOTE=schickel;284098]Not really. Some of the queries available were discussed over in the FactorDb thread, but I would say that the only one who knows what all is available is Syd....[/QUOTE]
I kind of wondered if there was a .php method that queries available functions.
[QUOTE=schickel;284098]I have been thinking along those lines, too. So far it seems to me there is no really easy way to do things, since if you want to make it comprehensive, you almost have to have 1.000.000 entries (less the primes since they're easy), even if most of them are "S[sub]n[/sub] merges with x after y lines" or "S[sub]n[/sub]terminates in x after y lines" with y<10.....[/QUOTE]Yeah, I was thinking along the lines of a list:
[code]
seq1:line = seq12:line
seq1:line = seq23:line
seq34:line = seq44:line
...
[/code]But, let's address two sequences that end in the same cycle. Did they merge?

This is seeming more complex, the further I dig...

 schickel 2011-12-31 06:23

[QUOTE=EdH;284191]Wow, I guess I've been around for two years now, according to my stats... But I should still be considered as someone who doesn't know much.:smile:

The more I look at this, the larger a task it seems. To download 1M .elfs, or even just last lines, is a huge endeavor, itself. Even If I d/l 1k per day, it would take 3 years to complete...[/quote]Yeah, but the trick is, I just do the open ones, and there are only [strike]9244[/strike] 9243 open ones. I have it broken into 3 parts because I have a memory leak somewhere that kills the task after ~6000 downloads. It takes about 4 hours to do each 1/3 of the list. (Most of the time is spent reformatting the files a little; if you pad the line numbers out to 10 spaces, you can peg the size of a line easier.)[quote]
I'm going to have to think a bit more about this. Things like maybe I should eliminate those sequences that end in primes or cycles.[/quote]Eliminate from the download? Yes, you can, since they're done once they merge....[quote]
It would be easier to parse the .elf files, although they would be larger.[/quote]That's true, though the download time would be lots less just for the last line.[quote]I kind of wondered if there was a .php method that queries available functions.[/quote]Nothing was ever brought up about that. It looked like Syd was adding stuff as people brought things up.[quote]Yeah, I was thinking along the lines of a list:
[code]
seq1:line = seq12:line
seq1:line = seq23:line
seq34:line = seq44:line
...
[/code]But, let's address two sequences that end in the same cycle. Did they merge?[/quote]I would look at where they merged. If they merge [I]before[/I] the resulting confluence hits the cycle, I would say that was a merge, since there was some activity before the merge.

This actually came up on one of our terminations. I marked it as a merge because it hit a sequence and headed up before the last downdriver run to the termination. Wolfgang marked it down as a temination since it actually terminated rather than ran into another open sequence.[quote]This is seeming more complex, the further I dig...[/QUOTE]Welcome to our world....:grin:

------------------------

The ultimate solution is to draw a tree where each number is a node with an arrow pointing to its $$\sigma(n)-n$$ value and has arrows pointing from numbers that point to it.

After this post, I'll look back; someone was here wondering what software to use to visualize aliquot cycles in this manner, and I think they posted a paper, with some of the aliquot trees in it. Unfortunately, I forgot where I found it.....:face palm:

 schickel 2011-12-31 06:26

Here's the [URL="http://www.mersenneforum.org/showthread.php?t=15538"]thread[/URL] I was thinking of. Geez.....it was only in April that this came up.

Now I'll go and see if I can find that paper.

 schickel 2011-12-31 06:53

Aha! Here we go. Richard Mathar at Leiden University; here is an [URL="http://www.strw.leidenuniv.nl/~mathar/public/"]index[/URL] of his papers, and here's a deep link to the [URL="http://www.strw.leidenuniv.nl/~mathar/public/mathar20100305.pdf"]paper[/URL] I was thinking of....

[Edit: I wonder if this is the first citation of the FactoDB in a paper.....]

 schickel 2011-12-31 08:19

[QUOTE=schickel;284194]After this post, I'll look back; someone was here wondering what software to use to visualize aliquot cycles in this manner, and I think they posted a paper, with some of the aliquot trees in it. Unfortunately, I forgot where I found it.....:face palm:[/QUOTE]OK, so it looks like it wasn't the same person....I wonder if [B]Wini[/B] left a working email on file....

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