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Old 2022-03-16, 21:33   #1
EdH
 
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"Ed Hall"
Dec 2009
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Default Some Somewhat Easier n^i Sequences Available for Termination

In the sub-project Aliquot sequences that start on the integer powers n^i, there are some sequences becoming available that should terminate with a prime and are currently (or will be) only around 100-130 145 digits in size.* These sequences are mostly above those of the main project, although some may drop into the main project on their way to termination.**

If you are interested in the excitement of terminating an Aliquot Sequence, although not guaranteed, these are pretty sure bets to do so.

Note: For anyone, new or old that would like to automate some of their work, please look at the script in post 7 below. The script can be used with Aliqueit to convert the base^exponent value to its decimal and invoke Aliqueit to run the sequence and upload the results.

Please visit the above thread and the Main Project Page for more details. You may reserve the available sequences in this thread and see the current status on the project page, as updates are applied.

As an example of an available sequence, 167^89 is the smallest as of the latest full edit, and has a 110 digit term with a composite cofactor of only 96 digits.

As of the time of the last edit (fiddling), the following sequences are available:
Code:
10^150: 138/110
42^92: 144/140
46^90: 144/123
47^93: 132/104
57^85: 138/120
63^83: 142/141
68^82: 139/121
75^81: 144/136
80^78: 141/135
82^78: 124/99
84^78: 143/129
85^77: 141/127
92^76: 140/119
107^67: 131/131
107^69: 138/137
107^71: 140/135
107^73: 142/128
131^63: 131/121
131^65: 136/106
131^67: 136/125
131^69: 143/124
131^71: 130/116
139^57: 120/115
139^63: 133/103
139^65: 128/122
139^67: 119/117
139^73: 135/118
139^83: 142/111
149^57: 121/109
149^59: 124/113
149^63: 135/132
149^65: 137/137
149^67: 136/119
151^57: 122/102
151^59: 121/109
151^61: 128/125
151^63: 135/125
151^65: 139/128
151^67: 140/139
151^73: 133/122
157^57: 123/117
157^59: 125/119
157^61: 125/120
157^63: 136/112
157^65: 140/136
157^67: 134/103
157^73: 138/125
163^57: 124/110
163^59: 126/109
163^63: 138/122
163^65: 141/113
163^67: 142/142
163^89: 129/102
167^57: 123/108
167^63: 137/136
167^65: 137/120
167^67: 140/137
167^89: 110/96
210^64: 139/137
211^65: 140/114
220^64: 144/116
276^62: 130/126
564^54: 137/122
648^53: 144/104
966^50: 144/123
1058^50: 144/135
1152^37: 113/109
1152^39: 117/103
1152^40: 122/103
1152^41: 125/100
1152^42: 129/120
1152^43: 132/130
1152^44: 136/121
1152^45: 139/111
1152^46: 142/126
1152^47: 144/126
1152^48: 139/138
1250^40: 124/112
1250^41: 128/128
1250^42: 130/112
1250^43: 133/124
1250^44: 137/110
1250^45: 140/138
1250^46: 142/139
1250^47: 129/118
1250^48: 141/117
2310^46: 143/109
12496^36: 138/110
14264^36: 144/143
510510^26: 140/108
The second value is the cofactor size.

Here's a size sorted listing of the above. If this doesn't take too much work, I'll keep updating it:
Code:
167^89: 110/96
1152^37: 113/109
1152^39: 117/103
139^67: 119/117
139^57: 120/115
149^57: 121/109
151^59: 121/109
151^57: 122/102
1152^40: 122/103
167^57: 123/108
157^57: 123/117
163^57: 124/110
1250^40: 124/112
149^59: 124/113
82^78: 124/99
1152^41: 125/100
157^59: 125/119
157^61: 125/120
163^59: 126/109
139^65: 128/122
151^61: 128/125
1250^41: 128/128
163^89: 129/102
1250^47: 129/118
1152^42: 129/120
1250^42: 130/112
131^71: 130/116
276^62: 130/126
131^63: 131/121
107^67: 131/131
47^93: 132/104
1152^43: 132/130
139^63: 133/103
151^73: 133/122
1250^43: 133/124
157^67: 134/103
139^73: 135/118
151^63: 135/125
149^63: 135/132
131^65: 136/106
157^63: 136/112
149^67: 136/119
1152^44: 136/121
131^67: 136/125
1250^44: 137/110
167^65: 137/120
564^54: 137/122
167^63: 137/136
149^65: 137/137
10^150: 138/110
12496^36: 138/110
57^85: 138/120
163^63: 138/122
157^73: 138/125
107^69: 138/137
1152^45: 139/111
68^82: 139/121
151^65: 139/128
210^64: 139/137
1152^48: 139/138
510510^26: 140/108
211^65: 140/114
92^76: 140/119
107^71: 140/135
157^65: 140/136
167^67: 140/137
1250^45: 140/138
151^67: 140/139
163^65: 141/113
1250^48: 141/117
85^77: 141/127
80^78: 141/135
139^83: 142/111
1152^46: 142/126
107^73: 142/128
1250^46: 142/139
63^83: 142/141
163^67: 142/142
2310^46: 143/109
131^69: 143/124
84^78: 143/129
648^53: 144/104
220^64: 144/116
46^90: 144/123
966^50: 144/123
1152^47: 144/126
1058^50: 144/135
75^81: 144/136
42^92: 144/140
14264^36: 144/143
* Since most of the smaller sequences have been terminated, a new threshold of 145 digits has been established.

** Sequences of the type n^i where both n and i are either odd or even (matched parity) nearly always terminate. Also, sequences where n is double a perfect square nearly always terminate. On occasion one will merge with a sequence in the main project and become open-ended.

The following are the current reservations:
Code:

The following are the terminated sequences that have not yet been updated in the tables. Many have unknown credit for termination (listed as A). If the terminator would like credit, please claim it in this or the other thread:
Code:
19^137: Prime - A
167^59: Prime - GDB
1250^36: Prime - A
1250^38: Prime - GDB
1250^39: Prime - GDB

Last fiddled with by EdH on 2022-05-15 at 23:41
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Old 2022-03-16, 23:55   #2
RichD
 
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I went through some of my recent initializations and found a few that might be worthy to elevate into the first post.
Code:
84^66: 128/104
84^68: 132/116
84^70: 136/119
86^66: 128/115
86^68: 131/128
86^70: 136/122
90^68: 134/129
91^65: 127/120
91^67: 131/107
91^69: 135/122
92^62: 122/94
92^64: 126/115
92^66: 130/113
92^68: 134/99
93^65: 128/101
93^67: 131/103
93^69: 136/108
95^63: 124/116
95^65: 129/100
95^67: 133/119
95^69: 136/124
96^66: 132/118
96^68: 136/128
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Old 2022-03-17, 00:20   #3
EdH
 
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Thanks Rich,

I hadn't planned to make this a new source, but maybe that would work. I'll try to keep up with new available sequences, at least for now.

If we can get some more interest, the newcomers can also initialize some bases and work both terminations and open-ended, too.
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Old 2022-03-17, 02:35   #4
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I'll help with administration on this thread- updating post 1 with reservations, etc.
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Old 2022-03-17, 12:32   #5
kruoli
 
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If appropriate, I would like to take these:
Code:
3^333: 134/123
84^70: 136/119
86^70: 136/122
90^68: 134/129
91^69: 135/122
92^68: 134/99
93^69: 136/108
95^69: 136/124
96^68: 136/128
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Old 2022-03-17, 14:07   #6
EdH
 
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Perhaps we should discuss which direction to take this thread, and how to minimize confusion with the main thread.

My initial vision was to have a few smaller sequences available to introduce newcomers to the project at a level they could work with a single machine.

As it now looks, we could create a large set of available sequences, much larger than my original thoughts. This could easily spiral into a mass of confusion for us. We need to keep this coordinated with Jean-Luc and not task him too heavily.

We need also to consider yoyo in this, since he'll be needing <140 work for his hungry project.

Let's step back momentarily to prioritize project goals. We'll need Jean-Luc to help with this. Advancing the tables is going to be more intensive due to how fast the terms now get large. How does table advancement, vs. same parity termination, vs. new table additions work toward the goals that provide the data for the questions that drive this project?

My proposals, for now:
- We hold only a very few to attract newcomers and see if we do. (we need to decide how few, etc.)
- We should go ahead and terminate the rest among ourselves as we would normally do.
- - kruoli has asked for some. I'm OK with that and they aren't reserved in the tables, but I would also like input from RichD, since he provided the bulk of them.*
- - VBCurtis also expressed interest in the ones I'm bringing below 140 digits. Let's go ahead and let our members reserve and work these as we have been.*
- I'm hesitant due to workload and confusion, but we may want to use the first post as a reference to smaller, same parity, available sequences. I would accept all help in that upkeep, but again, I'd like to minimize confusion with the main thread and Jean-Luc, so the table workings don't get too complicated. Keeping up with reservations could become duplication of effort and confusion if it isn't timely.

* We still need to use the other thread for reservations so the tables get updated and I'll move any reservation posts from this one over once we've discussed this a little more. We could be more timely showing reservation status here, but would it conflict with those on the main table pages?

All comments welcome. . .
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Old 2022-03-17, 14:51   #7
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If we want to attract new personnel, I would suggest we take their hand a bit (at least give the possibility) and give some guiding on how to execute this work. For example, I prepared a small script for this thread:
Code:
export BC_LINE_LENGTH=0; # disable line breaks in bc
bc < list.txt > list.bc;
line_count_input=$(wc -l < list.bc);
base_dir=../terminations;

rm -f *.log siqs.dat nfs.*;
for i in $(seq 1 $line_count_input);
do
  number=$(sed "${i}q;d" list.bc); # use this instead of read line (etc.) to prevent a misdeteciton of file redirection in YAFU, which would enter batch mode and cause problems
  alq_file=alq_${number}.elf;
  wget -O $alq_file "http://factordb.com/elf.php?seq=${number}&type=1";
  line_count_elf=$(wc -l < $alq_file);
  ./aliqueit -y $number | tee execution.log; # use tee to see the progress while still logging to a file
  ./aliqueit -s $(($line_count_elf-1)) $number > upload.log; # maybe check if upload limit was reached here
  dir=$base_dir/$(sed "${i}q;d" list.txt);
  mkdir $dir;
  mv -t $dir aliqueit.log execution.log upload.log $alq_file;
done;
Put your work in a file named list.txt, one entry per line in the form x^y. It is assumed that you have an aliqueit executable in the same directory as the script (optimally with aliqueit.ini and yafu.ini if you have configured aliqueit to use YAFU as it would be recommended). Additionally, you would need wc, wget, sed and bc (these do not come with every Linux distribution by default). It will get the current ELF files and upload the results immediately after a sequence has terminated. The results will be stored as condfigured by base_dir. (One could add another parameter to aliqueit to prevent getting in the rare case of a sequence not ending trivially.)

We could add links to threads (e.g. EdH's) on how to set up and compile YAFU(2) and aliqueit.

As an aside, how do you pronounce aliqueit? Like ah-lee-kweet?

Last fiddled with by kruoli on 2022-03-17 at 14:56 Reason: Fixed a typo.
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Old 2022-03-17, 15:43   #8
EdH
 
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Quote:
Originally Posted by kruoli View Post
If we want to attract new personnel, I would suggest we take their hand a bit (at least give the possibility) and give some guiding on how to execute this work. For example, I prepared a small script for this thread:
. . .
We could add links to threads (e.g. EdH's) on how to set up and compile YAFU(2) and aliqueit.

As an aside, how do you pronounce aliqueit? Like ah-lee-kweet?
This could be a great idea, especially if we get anyone at that beginning of a level. I would hope the script wouldn't look too complicated to them. We can add this to the first post once we have a clear direction.

My pronunciation, which is actually rarely vocal, is more ah-leh-cue-it, but the ah still isn't quite right. I don't know the author's version.
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Old 2022-03-17, 16:36   #9
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Perhaps it is I that has the misunderstanding. For a newbie to look at the main status table is a bit overwhelming. For the rest of us that grew up with it, it is easy to understand.

I mostly do initialization work. Take sequences up to C100. If they start bigger, I take the (expected) terminating ones from C118-C120 to termination. I leave several in the C120-C140 range and above.
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Old 2022-03-17, 18:44   #10
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Thank you very much Edwin for taking care of this and thank you very much to all the other people who are taking part in this new venture concerning n^i sequences with n and i of the same parity (matched parity) and with i large enough to require a good computing power.
I don't know at the moment if I have a role to play in this thread ?
I think the easiest way to avoid any confusion is indeed for you to let me know about your reservations on the main project thread, that's what I understand ?
Then I will update the project page according to these reservations.
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Old 2022-03-17, 22:24   #11
RichD
 
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My (two cents) thoughts are, we would have a list of terminating candidates in post #1. People would speak up here to reserve a few. No need to flag them in post #1, simply remove them from the availability list. As more are spotted they can be added. We should never deplete the list, always leave a few.

Since the termination runs usually last less than a day (or so), no need to flag them here. As they complete they should be reported in the main thread for proper credit. This thread is for add and subtract.

More thoughts welcome.
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