Some Somewhat Easier n^i Sequences Available for Termination

[EdH]

In the sub-project Aliquot sequences that start on the integer powers n^i, there are some sequences that should terminate with a prime. This thread will list those with a current term that is less than 145 digits* and flagged as unreserved. 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 thread mentioned above and its associated page for more details. You may reserve the available sequences in this thread and see the current status on the project pages, as updates are applied.

As an example of an available sequence, 223^57 is the smallest as of the latest full edit, and has a 130 digit term with a composite cofactor of only 125 digits.

It is suggested that if you will take more than a day (or two) to terminate a sequence, you reserve it, so others don't duplicate your work. The following are the current reservations (but, also check the latest posts):

12^148: 135/121 - richs

As of the time of the last edit (fiddling), the following sequences were available:

10^158: 144/132 - last matched parity sequence for this base
12^144: 135/127
15^131: 143/137
20^104: 132/130
20^108: 141/123
20^110: 144/140
20^112: 144/134
21^101: 133/122
21^107: 142/134
21^111: 140/137
22^102: 135/132
22^104: 140/136
22^106: 143/132
22^108: 143/134
23^107: 138/130
23^109: 138/132
24^102: 141/141
24^104: 144/134
24^106: 143/125
26^102: 143/128
29^103: 142/138
29^109: 144/125
31^109: 142/133
34^100: 141/129
37^101: 138/138
37^109: 144/121
42^92: 143/126
43^97: 137/135
43^99: 144/126
44^92: 132/129
44^94: 144/142
48^90: 142/127
52^98: 142/135
77^75: 132/128
78^76: 144/124
80^78: 141/135
85^77: 141/127
87^73: 138/135
87^75: 139/128
87^77: 144/120
88^68: 133/130
88^72: 139/127
88^74: 138/128
88^76: 142/126
93^77: 142/140
94^70: 138/130
94^72: 143/124
94^76: 143/120
96^76: 135/126
97^81: 138/132
107^69: 138/137
107^73: 137/133
109^69: 137/120
113^73: 144/130
151^69: 136/134
157^63: 133/130
157^73: 137/125
163^63: 137/131
163^69: 144/144
167^69: 138/126
167^75: 143/143
173^71: 143/126
191^65: 144/139
193^63: 142/127
197^63: 139/131
197^65: 137/130
197^71: 138/123
199^63: 140/133
199^65: 144/136
199^67: 142/137
223^57: 130/125
227^59: 130/130
233^59: 132/129
233^63: 132/122
233^65: 142/141
233^73: 133/131
338^62: 144/144
385^63: 143/132
882^51: 143/127
882^54: 135/131
1152^43: 132/130
1152^45: 138/128
1152^46: 142/126
1152^49: 138/128
1152^50: 139/124
1250^44: 135/122
1250^45: 140/138
1250^48: 137/131
1250^50: 137/137
14264^36: 144/131
14536^36: 141/131
510510^26: 139/126
223092870^20: 141/132 - last matched parity sequence for this base

The second value is the cofactor size.

Here's a size sorted listing of the above:

223^57: 130/125
227^59: 130/130
233^63: 132/122
77^75: 132/128
44^92: 132/129
233^59: 132/129
20^104: 132/130
1152^43: 132/130
21^101: 133/122
88^68: 133/130
157^63: 133/130
233^73: 133/131
1250^44: 135/122
96^76: 135/126
12^144: 135/127
882^54: 135/131
22^102: 135/132
151^69: 136/134
109^69: 137/120
157^73: 137/125
197^65: 137/130
163^63: 137/131
1250^48: 137/131
107^73: 137/133
43^97: 137/135
1250^50: 137/137
197^71: 138/123
167^69: 138/126
88^74: 138/128
1152^45: 138/128
1152^49: 138/128
23^107: 138/130
94^70: 138/130
23^109: 138/132
97^81: 138/132
87^73: 138/135
107^69: 138/137
37^101: 138/138
1152^50: 139/124
510510^26: 139/126
88^72: 139/127
87^75: 139/128
197^63: 139/131
199^63: 140/133
22^104: 140/136
21^111: 140/137
1250^45: 140/138
20^108: 141/123
85^77: 141/127
34^100: 141/129
14536^36: 141/131
223092870^20: 141/132
80^78: 141/135
24^102: 141/141
88^76: 142/126
1152^46: 142/126
48^90: 142/127
193^63: 142/127
31^109: 142/133
21^107: 142/134
52^98: 142/135
199^67: 142/137
29^103: 142/138
93^77: 142/140
233^65: 142/141
94^76: 143/120
94^72: 143/124
24^106: 143/125
42^92: 143/126
173^71: 143/126
882^51: 143/127
26^102: 143/128
22^106: 143/132
385^63: 143/132
22^108: 143/134
15^131: 143/137
167^75: 143/143
87^77: 144/120
37^109: 144/121
78^76: 144/124
29^109: 144/125
43^99: 144/126
113^73: 144/130
14264^36: 144/131
10^158: 144/132
20^112: 144/134
24^104: 144/134
199^65: 144/136
191^65: 144/139
20^110: 144/140
44^94: 144/142
163^69: 144/144
338^62: 144/144

* The current threshold of 145 digits was chosen to ensure the listing has at least a fair number of sequences, with some more challenging.

** 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 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:

6^210: Prime - RCH - finishes this base
10^156: Prime - GDB
10^160: Prime - RCH
11^153: Prime - RCH -\
11^155: Prime - GDB - finishes this base
11^159: Prime - GDB -/
12^150: Prime - GDB
14^138: Prime - GDB -\
14^140: Prime - GDB - finishes this base
20^116: Prime - GDB
21^117: Prime - GDB
23^125: Prime - GDB
24^110: Prime - GDB
37^103: Prime - GDB
39^105: Prime - GDB
76^82: Prime - GDB
85^81: Prime - GDB
107^77: Prime - GDB
151^67: Prime - GDB
157^71: Prime - GDB
199^57: Prime - GDB
223^65: Prime - GDB
227^57: Prime - GDB
229^57: Prime - GDB
229^61: Prime - GDB
229^63: Prime - GDB
233^53: Prime - GDB
233^55: Prime - GDB
233^57: Prime - GDB
722^57: Prime - GDB

[RichD]

I went through some of my recent initializations and found a few that might be worthy to elevate into the first post.

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

[EdH]

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.

[VBCurtis]

I'll help with administration on this thread- updating post 1 with reservations, etc.

[kruoli]

If appropriate, I would like to take these:

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

[EdH]

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. . .

[kruoli]

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:

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?

[EdH]

Originally Posted by kruoli

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.

[RichD]

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.

[garambois]

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.

[RichD]

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.