Aliquot sequences that start on the integer powers n^i

[garambois]

OK, no problem, thanks.
I should have thought about it.

[EdH]

Originally Posted by garambois

I just started running my own program.
I hope we will have the same result !
I also hope there won't be new broken sequences.
Result in a few days, I confirm, it is going much faster than a year ago.
What happiness !
It is even now possible to scan a main project which would consider all sequences <10^7 !

I'm looking forward to your results.

After I "fixed" the two broken sequences in my local set, I did a full test with Aliqueit again. I expect that they are not fixed yet in the db, so you should find them. But the corrected ones are a few posts back.

Still, I think it took me more than 48 total hours for 27.5k+ sequences. If my math is correct (often not the case), that would still be nearly 2 years for <10^7. . .

[garambois]

Originally Posted by EdH

Still, I think it took me more than 48 total hours for 27.5k+ sequences. If my math is correct (often not the case), that would still be nearly 2 years for <10^7. . .

2 years ? 2-3 days to scan the main project down to 3 * 10^6 so about roughly 27,000 or let's round up to 30,000 sequences.
So up to 10 * 10^6 = 10^7 so about 90,000 sequences, it takes about 6 days or a week, right ?

[EdH]

Originally Posted by garambois

2 years ? 2-3 days to scan the main project down to 3 * 10^6 so about roughly 27,000 or let's round up to 30,000 sequences.
So up to 10 * 10^6 = 10^7 so about 90,000 sequences, it takes about 6 days or a week, right ?

My confusion is that I was thinking of total sequences, whereas I "think" you are referring to open sequences. Do you have a listing of open sequences between 3M and 10M? If all are to be retrieved and checked for status, that's still 7M.

[Happy5214]

Originally Posted by garambois

I have to admit that I am starting to confuse the basics, because there are a lot of them now.
The advantage of the current presentation is that the numbers are arranged in ascending order.
I don't know if I understand your entire message correctly.
If I understand correctly, you are suggesting to leave as it is now, but to add buttons to click at the beginning of the page, on which we could click.
These buttons would be titled "primorial", "perfect", "cycles", '2 times a square ", ....
And when we click on these buttons, it would only reveal the bases included in the category.
Is that your idea ?
I think it's a very good idea !

On the other hand, I am totally unable to realize the code to do this. I will have to ask the great architect of the page, Karsten Bonath, that I do not can never thank enough for all his help.
Can you confirm to me that I understand your idea correctly ?
Does anyone else have an opinion on this matter ?

Sorry, I tend to ramble to a point that non-native English speakers (and some native speakers) can't understand me.

Sort of. I'll write some mock-ups of my ideas and post them as attachments.

[garambois]

Originally Posted by EdH

My confusion is that I was thinking of total sequences, whereas I "think" you are referring to open sequences. Do you have a listing of open sequences between 3M and 10M? If all are to be retrieved and checked for status, that's still 7M.

Yes, I have such a list in my fundamental database and I even have this list up to 14,000,000.
This is the file called "regina_opens.tar.lzma" here :
http://www.aliquotes.com/aliquote_base. htm # alibasefonda
But the problem is that in this database, I consider a sequence to be Open-End as soon as the size of its terms first reaches 10^50.
There are just over 142,000 Open-End sequences up to 14,000,000 in my database.

[garambois]

Originally Posted by Happy5214

Sorry, I tend to ramble to a point that non-native English speakers (and some native speakers) can't understand me.

Sort of. I'll write some mock-ups of my ideas and post them as attachments.

Ok thank you !
Being non-English speaking, I also wonder if sometimes you have no trouble understanding what I'm saying.
I trust machine translation a lot !

[EdH]

Originally Posted by garambois

Yes, I have such a list in my fundamental database and I even have this list up to 14,000,000.
This is the file called "regina_opens.tar.lzma" here :
http://www.aliquotes.com/aliquote_base. htm # alibasefonda
But the problem is that in this database, I consider a sequence to be Open-End as soon as the size of its terms first reaches 10^50.
There are just over 142,000 Open-End sequences up to 14,000,000 in my database.

Then that seems much more doable. Now that you mention this, I remember it from some time quite a while ago. But, I couldn't bring it to the forefront yesterday. Sorry to be such an annoyance at times. . .

[garambois]

I would also like to warmly thank Karsten Bonath for all the help he gives me in writing the lines of code that generate the reservations page.
I will be saving a lot of time with some new and recent scripts !
This well done and readable page is fundamental in our project.
It greatly contributes to the good visualization of the data in order to then correctly orient the more in-depth data analyzes and to know what calculations we have to do.

[Happy5214]

Here are the mock-ups. I decided against splitting up the data due to the categorical overlap. There are four levels of progression from the existing HTML file. powers.html shows the file with the proper semantic HTML markup I brought up several months ago, including <h2> headers and <section> tags for the base sections, renamed CSS classes to reflect usage rather than color, using <var> tags for the variables instead of <i> (or nothing at all in some cases), and enclosing text in <p> paragraph tags. powers1.html simply adds a new <h2> heading for the bases and converts the individual base headers to <h3>. powers2.html moves the table open/close button after the header in the HTML code for semantic reasons and floats it to the left to achieve the same display effect. powers3.html actually adds the navigation table, which is simply a two-row table with the header and lists as the second row. Most lists are ordered, adding additional structure to the series categories. The visual appeal needs some work, though the idea is basically what is shown.

Edit: I did just realize that the navigation header styling doesn't match. That's a simple CSS fix.

[garambois]

Now I understand your idea better.
And I think your idea for the "powers3" html file would bring more clarity to the page and make it easier to exploit the results.
Do you think it would be useful to add the possibility of clicking on the column headers of the "Navigation" table so that only the bases of a single category appear ?
For example, we could click on "Perfect" in the header of the fourth column and that would open the html page that I present below (see "Attached Files").
Thus, one would more easily notice properties specific to perfect numbers.
These html pages for each of the categories are easy for me to generate.
Unless these other pages are not necessary and we can only display the bases of a single category while hiding all the others ?
On the other hand, I do not understand your comments on the tags.
This is completely outside my area of ​​expertise.
I leave that to the specialists (I also tell myself that the other html pages of my own site must be frankly "disgusting" for a specialist !).

Small detail : should 6 appear in the "others" column ?