Novice Questions About Merges

[EdH]

Is there a way to query the db to find out what numbers merge with a base number? For instance, there are at least 5 numbers that merge with 4788: 314718, 244384, 212712, 33552 and 6102. These are based on merges through the chain of these shown. Are there other numbers that merge with 4788? Since it is the lowest, you can't see any from the 4788 page.

A number is considered finished, workwise, if it merges, but a termination is better. When looking for a new sequence for Team effort, would a number which has lots of merges be of any more interest, since, if it terminates, it will terminate all the others?

Would a number that has lots of merges, be any more apt to cycle?

Thanks,
Ed

[kar_bon]

W.Crayaufmüller got on his site in the section "Databases" a
file "C9C30 complete version" for download (last update Aug.2009).
This file contains all seqs <1M with terminations and side-sequences.

For example the first entry with 4788-side:

s 42800X 102173099844589017001826781552  691 S-C9X: 4788

So the index 691 from seq 42800 is equal to a C30 from 4788.

[Mini-Geek]

Originally Posted by EdH

A number is considered finished, workwise, if it merges, but a termination is better. When looking for a new sequence for Team effort, would a number which has lots of merges be of any more interest, since, if it terminates, it will terminate all the others?

I'm not sure if a sequence with lots of merges carries any more interest to terminate. Obviously, the answer to that question depends on whether you consider a sequence ending in a prime fundamentally different from one ending in a merge.

Originally Posted by EdH

Would a number that has lots of merges, be any more apt to cycle?

Yes, but of course this is only due to its "branches" meaning that there are more past values to collide with. (e.g. if a sequence is formed from 10 merges averaging a length of 100 before merging, it's like you've got another 1000 indexes to potentially merge/cycle with) I don't know how much more this would, on average, increase the chances of a cycling being discovered, but I'd say it's by a very large proportion. After all, the side sequences (probably) don't just add a few 60+ digit numbers, which are so sparsely-encountered as to practically never coincide, but they (probably) add dozens of small numbers, which are far more likely to coincide with future indexes.

[EdH]

kar_bon,

Thank you for the link. Am I correct that this is only those members of the 4788 "family" that coincide with a c9 or c30? Did I miss something somewhere on the site that would show the entire 4788 family? From my quick search of the db, using the c9/c30 data and the subsequent numbers (as well as others I was aware of), I have turned up over twenty additional numbers that merge (eventually) with 4788. My list currently includes:

6102
8092
10912
21818
33552
35386
42800
61762
63974
70568
80632
95952
122074
137280
144592
212712
244384
245050
225626
274846
275576
314718
398138
416304
428960
509562
533700
614570
633096
765264
870968
939968
977802

Originally Posted by Mini-Geek

I'm not sure if a sequence with lots of merges carries any more interest to terminate. Obviously, the answer to that question depends on whether you consider a sequence ending in a prime fundamentally different from one ending in a merge.

I suppose I do, since it is not terminated if the base number isn't.

Originally Posted by Mini-Geek

Yes, but of course this is only due to its "branches" meaning that there are more past values to collide with...

This was my thought, but wondered if there was more to it, or whether the odds were affected in any great amount, obviously realizing they would be better at lower sizes.

I could easily write a script that could query the db for all the numbers that merge into 4788, but ~.5M hits would just add to the delay in working through other tasks. Maybe some time I'll try a few at a go and see what I come up with.

I do find it interesting that so many numbers' sequence's fate can rest on a single base...

Thanks,
Ed

[10metreh]

Sequence 6160 (terminated in 2001) had LOADS of side-sequences that terminated with it.

Note: In case you're wondering how a sequence can terminate with 6160, I mean that when 6160 terminated, its >1000 side-sequences below 1M did too.