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Old 2021-06-02, 12:10   #1134
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Quote:
Originally Posted by garambois View Post
This is already special, since we have so few.
But what would be really special is if there were another exponent of 14316 that ended in a cycle of length other than 1.
This is what we are looking for, since so far this has only happened for bases that are perfect numbers.
And this must really be due to pure chance !
But I must admit that I didn't look at 14316.
Also note that all 28 values in the 28-cycle are possible start values for the cycle. 14316 is just the lowest. They should all eventually be tested as bases if we're going to do organized work on higher-order sociable number cycles. There's also the (based on current knowledge) single 5- and 9-cycles, 5 6-cycles, and 4 8-cycles, as well as 5k+ 4-cycles. (Numbers based on Wikipedia.) We won't do all of the 4-cycles, but the others might be attainable.

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Originally Posted by garambois View Post
Thank you very much for doing the preliminary work up to exponent 63. That's exactly what we needed to do.
The reason I mentioned exponent 100 is because yoyo routinely runs all calculations up to exponent 100.
So when I add a new base < 100 on our project page, I now routinely set the exponent to 100.
For higher bases, I put exponents smaller and smaller as the base becomes larger.
Anyway, even yoyo will never do calculations for terms larger than 150-160 digits.
And I understand that many people do calculations for our project, because the size of the numbers is still not too big compared to the main project.
But after the preliminary work, some of us will reserve the base and may want to finish some trivial exponents for some bases and indeed, also to take the term size up to 120 digits for the open-ends sequences, or even 140 digits.
I also thought that some people with a lot of computing power might want to push the work a bit further even for the preliminary phase, for example for exponents that end trivially.
That's why I recalled that the exponents go to 100 for bases < 100.
If you feel like pushing the preliminary work a bit further, but only if you find pleasure in it, that's our rule, I think it's better to act on sequences that end trivially than open-ends.
And this is in view of the future analyses in August.
But maybe other people see it differently and will ask the opposite...
OK, I'll do the trivial sequences for base 39 up to 120 digits (and maybe a bit beyond, depending on how reasonable the cofactors are for the few sequences afterward).
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Old 2021-06-02, 19:44   #1135
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Updated and modified page.

Thanks to all for your help.
Many thanks to Andrey Chechevatov for pointing out 4 missing merges for sequences 33^22, 38^41, 42^35 and 43^52.

Many thanks to Karsten Bonath who once again did a lot of work to bring new features to our page, according to some requests in previous posts.
We let you test it.
Please report any malfunctioning to us.

Note : The sorting-by-keyboard is included: use TAB key to browse the header cells, too and use RETURN to change sorting (as Happy suggested).



Quote:
Originally Posted by Happy5214 View Post
OK, I'll do the trivial sequences for base 39 up to 120 digits (and maybe a bit beyond, depending on how reasonable the cofactors are for the few sequences afterward).
OK, many thanks.
So I will add base 39 later.
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Old 2021-06-02, 20:04   #1136
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Quote:
Originally Posted by Happy5214 View Post
Also note that all 28 values in the 28-cycle are possible start values for the cycle. 14316 is just the lowest. They should all eventually be tested as bases if we're going to do organized work on higher-order sociable number cycles. There's also the (based on current knowledge) single 5- and 9-cycles, 5 6-cycles, and 4 8-cycles, as well as 5k+ 4-cycles. (Numbers based on Wikipedia.) We won't do all of the 4-cycles, but the others might be attainable.

Even if we don't do the 4-cycles, the amount of work is still huge !
For the 28-cycle alone, that would be 28 bases !

As a first step, maybe we could try to add already the 14316 base and maybe also the 12496 base, the smallest number of the only known 5-cycle.
This way we would see if there is anything special going on.
The work could be done up to exponent 40 for both bases, it seems reasonable.
Does anyone want to do the preliminary work for these two bases ?
(If someone wants to do the preliminary work for the 28+5=33 bases of all the numbers belonging to these two cycles, I'm interested ;-) )
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Old 2021-06-03, 04:44   #1137
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Quote:
Originally Posted by garambois View Post
Many thanks to Karsten Bonath who once again did a lot of work to bring new features to our page, according to some requests in previous posts.
We let you test it.
Please report any malfunctioning to us.

Note : The sorting-by-keyboard is included: use TAB key to browse the header cells, too and use RETURN to change sorting (as Happy suggested).
See WCAG Failure F78, which applies here. In short, the header border is hiding the keyboard focus indicator (meaning the user doesn't know which column they're sorting), thus failing criterion 2.4.7 (focus visible). While that's technically Level AA and we're only claiming to meet Level A, that's still something we should fix, probably using CSS to either recolor or dash a focused header border.

Quote:
Originally Posted by garambois View Post
Even if we don't do the 4-cycles, the amount of work is still huge !
For the 28-cycle alone, that would be 28 bases !

As a first step, maybe we could try to add already the 14316 base and maybe also the 12496 base, the smallest number of the only known 5-cycle.
This way we would see if there is anything special going on.
The work could be done up to exponent 40 for both bases, it seems reasonable.
Does anyone want to do the preliminary work for these two bases ?
(If someone wants to do the preliminary work for the 28+5=33 bases of all the numbers belonging to these two cycles, I'm interested ;-) )
I'll provisionally take those two lowest bases for preliminary work, and I'll do them before base 40. This is assuming I don't run into any overheating issues on my laptop with the 100-120 digit base 39 trivial sequences. A recent kernel update messed up the CPU throttling, and it's already had one emergency shutoff while running GIMPS.

Last fiddled with by Happy5214 on 2021-06-03 at 04:44
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Old 2021-06-03, 16:58   #1138
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Quote:
Originally Posted by Happy5214 View Post
See WCAG Failure F78, which applies here. In short, the header border is hiding the keyboard focus indicator (meaning the user doesn't know which column they're sorting), thus failing criterion 2.4.7 (focus visible). While that's technically Level AA and we're only claiming to meet Level A, that's still something we should fix, probably using CSS to either recolor or dash a focused header border.
OK, try now.
Many thanks to Karsten.


Quote:
Originally Posted by Happy5214 View Post
I'll provisionally take those two lowest bases for preliminary work, and I'll do them before base 40. This is assuming I don't run into any overheating issues on my laptop with the 100-120 digit base 39 trivial sequences. A recent kernel update messed up the CPU throttling, and it's already had one emergency shutoff while running GIMPS.
Good luck to you.
I can't wait to see if we're going to have different behavior with these two new bases !
I don't think we will, but it's wise to check, we don't have to overlook this possibility...
Many thanks.
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Old 2021-06-04, 08:12   #1139
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Quote:
Originally Posted by garambois View Post
OK, try now.
Many thanks to Karsten.
That works, thanks!

Quote:
Originally Posted by garambois View Post
Good luck to you.
I can't wait to see if we're going to have different behavior with these two new bases !
I don't think we will, but it's wise to check, we don't have to overlook this possibility...
Many thanks.
Thanks to some Lincoln Logs left over from my childhood that are now propping up my laptop, I ran into no overheating issues with the remaining base 39 trivial sequences, so my reservations of the two cycle sequences above are now official. I'll start on those Friday or Saturday. Furthermore, thanks to favorable values that stayed below the 120-digit cofactor limit I usually use, I was able to do all of the base 39 trivial sequences up to 130 digits (39^81).
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Old 2021-06-05, 08:46   #1140
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Now that we have more room in the data table, I suggest adding columns for the numbers of open sequences over 140 digits and under 120 digits. We'll need a new background color for the latter (under 120); I suggest a simple plain white (#fff).
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Old 2021-06-05, 12:15   #1141
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14316 is initialized to 100 digits, and the trivial sequences are done to 120 digits (i=28). I'm going to attempt i=30, 32, and 34, assuming they fit in my 120-digit cofactor limit. i=30 is already at 120 digits and will be finished, and I'll see about the other two. Everything should be done Saturday or Sunday.
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Old 2021-06-05, 17:22   #1142
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Quote:
Originally Posted by Happy5214 View Post
Thanks to some Lincoln Logs left over from my childhood that are now propping up my laptop, I ran into no overheating issues with the remaining base 39 trivial sequences, so my reservations of the two cycle sequences above are now official. I'll start on those Friday or Saturday. Furthermore, thanks to favorable values that stayed below the 120-digit cofactor limit I usually use, I was able to do all of the base 39 trivial sequences up to 130 digits (39^81).
Quote:
Originally Posted by Happy5214 View Post
14316 is initialized to 100 digits, and the trivial sequences are done to 120 digits (i=28). I'm going to attempt i=30, 32, and 34, assuming they fit in my 120-digit cofactor limit. i=30 is already at 120 digits and will be finished, and I'll see about the other two. Everything should be done Saturday or Sunday.
OK, many thanks !
So I will add bases 39 and 14316 in the next update, in a few days or maybe the weekend of June 12 or 13 depending on my possibilities.
On my side, in the meantime, I try to color in green some cells of trivial sequences of bases 385 and 15015.
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Old 2021-06-05, 18:35   #1143
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Quote:
Originally Posted by Happy5214 View Post
Now that we have more room in the data table, I suggest adding columns for the numbers of open sequences over 140 digits and under 120 digits. We'll need a new background color for the latter (under 120); I suggest a simple plain white (#fff).
In post #1094, Karsten asked if we needed these additional statistics.
Three of us answered that we didn't need to add these statistics (see posts #1095, #1096 and #1097).

But maybe I don't understand your request ?
You would still like to include these statistics in the table and also those for Open-End sequences <120 digits, is that right ?

As far as I'm concerned, I haven't changed my mind, I still don't need to separate the Open-End sequence statistics into their three categories.
Please, may I ask what changed your mind, if it is indeed the case ?

Because I think it would be a pity to have to decrease the width of the "Decomposition" column again : on the contrary, maybe this column should be widened ?
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Old 2021-06-06, 00:44   #1144
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Quote:
Originally Posted by garambois View Post
In post #1094, Karsten asked if we needed these additional statistics.
Three of us answered that we didn't need to add these statistics (see posts #1095, #1096 and #1097).

But maybe I don't understand your request ?
You would still like to include these statistics in the table and also those for Open-End sequences <120 digits, is that right ?

As far as I'm concerned, I haven't changed my mind, I still don't need to separate the Open-End sequence statistics into their three categories.
Please, may I ask what changed your mind, if it is indeed the case ?

Because I think it would be a pity to have to decrease the width of the "Decomposition" column again : on the contrary, maybe this column should be widened ?
My point in the post you linked was more along the lines of "they should be alike". With the table now being full-width, there's a ton of empty space, even on my 1600×900 monitor. Perhaps, if it's not too hard, we could add a toggle (a checkbox or a button) that switches between the default view and an "expanded" view that replaces the open columns (or adds to them) with <120, 120-140, and >140 columns.
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