Aliquot Sequences Summary Page

[10metreh]

Originally Posted by Andi47

The status of "reserved", "available" and "terminated" is color-coded: yellow for reserved and light blue for available.

The Lehmer Five are saying "last editor: P. Zimmermann", but they are color-coded in light blue (meaning "available"). I checked with firefox and IE.

Ah, I see now.

[kar_bon]

i updated the Lehmer 5 reserved by P.Zimmermann (and 4788 and 130396).
the data i got was out of date and i was not sure if he works on it further.

need some time to make all things work/look fine because i'm not so familiar with drivers/guides or the current reservations (only out of this forum so far).

please post here, if there're any other errors.

attached a view of that page it should look like this. if not there's something not correct with the browser settings.

[schickel]

Originally Posted by kar_bon

i updated the Lehmer 5 reserved by P.Zimmermann (and 4788 and 130396).
the data i got was out of date and i was not sure if he works on it further.

I think they're currently low priority. If there were the interest, the forum could adopt them, too.

need some time to make all things work/look fine because i'm not so familiar with drivers/guides or the current reservations (only out of this forum so far).

Did you check the wiki article? It covers the main points about the drivers; just ask here if you have any questions.....

As far as reservations, to the best of my knowledge, we're alone in the field in the 100-200k range. Check this thread for the status of other ranges.....

please post here, if there're any other errors.

I didn't see anything right off hand. Nice work on the table.....

attached a view of that page it should look like this. if not there's something not correct with the browser settings.

[10metreh]

Errrm... 2^2*7 is not the downdriver.

[schickel]

4788 - 2⁷ * 3² is a guide, not a driver.

29772 - 2⁴ * 7 is a guide.

103296 - 2² * 3 is a guide.

112638 - 2² * 3² is a guide

115302 - 2⁶ * 3 is actually controlled by 2⁶ * 127

139314 - 2⁵ * 7 is a guide.

150096 - 2⁴ * 3 is a guide.

162126 - 2² * 3² * 5 is a guide.

[axn]

Originally Posted by schickel

4788 - 2⁷ * 3² is a guide, not a driver.
<snip>

Hmmm... Either my definition of guide is messed up or most of these are incorrect. What's the definition of driver/guide you're using?

  4788  2^7*3^2*17 Guide
  9708  2^2*7  Driver
 10212  2*3    Driver
 29772  2^4    Guide
 88662  2^2    Guide
100320  2^2*7  Guide
100436  2^4*31 Guide
103296  2^2    Guide
112638  2^2    Guide
115302  2^6*127 Driver
123960  2^2    Guide
128370  2^2    Guide
129336  2^2    Guide
132792  2^4*31 Driver
132920  2^4*31 Driver
139314  2^5*7  Guide
145008  2*3    Driver
149808  2^2*7  Driver
150096  2^4    Guide
162126  2^2    Guide
167148  2^4    Guide
168912  2^4    Guide
171018  2^2    Guide
175410  2*3^2  Driver
182224  2^4*31 Driver

[schickel]

Originally Posted by axn

Hmmm... Either my definition of guide is messed up or most of these are incorrect. What's the definition of driver/guide you're using?

Drivers are defined in this article:

R. K. GUY and J. L. SELFRIDGE, "What drives an aliquot sequence," Math. of Comp. v. 29, n. 129, 1975, pp. 101-107.

I'm not sure if my use of guide is correct, but I use "guide" for anything that persists, but that's not a driver.

The drivers outlined in the above article are:

 (the downdriver)

[10metreh]

Originally Posted by schickel

but I use "guide" for anything that persists, but that's not a driver.

What is the word Guy and Selfridge suggest using for things like 2^2*3, which would be classified as having the "guide" 2^2 (seems completely mad)?

[schickel]

Originally Posted by 10metreh

What is the word Guy and Selfridge suggest using for things like 2^2*3, which would be classified as having the "guide" 2^2 (seems completely mad)?

Here's the definition from the article:

Originally Posted by Guy&Selfridge

Define a guide to be , together with a subset of the prime factors of . A driver is defined as a number with , odd, and . The last requirement is included so that the power of the prime 2 will tend to persist at least as well as it does for the driver 2 itself, for which the condition is trivially satisfied.

Further down, they give these as guides:

So, I have been a little, um, imprecise, in calling, for example, , a guide. The guide is actually ...

And I actually have been lax: the drivers include the even perfect numbers.....

[axn]

Originally Posted by schickel

Drivers are defined in this article:I'm not sure if my use of guide is correct, but I use "guide" for anything that persists, but that's not a driver.

Ok. I get one definition of guide from here (PDF file).

Basically, what forms a driver or guide depends on the factorisation of Sigma(2^a).

EDIT:- Frank was here first :)

[schickel]

Originally Posted by axn

Ok. I get one definition of guide from here (PDF file).

Basically, what forms a driver or guide depends on the factorisation of Sigma(2^a).

EDIT:- Frank was here first :)

Yes, in the 3630 article, they give a quick review of the definition. If you're interested in the full proof, you have to go back to the Guy & Selfridge article.

If you have access to a library with inter-library loan privileges with a school, you can request a copy of the original article. (I got mine from a co-worker who was moonlighting from their day job at the local community college....)