mersenneforum.org Some Somewhat Easier n^i Sequences Available for Termination
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 2022-03-16, 21:33 #1 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 17×271 Posts 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 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): Code: 12^148: 135/121 - richs As of the time of the last edit (fiddling), the following sequences were available: Code: 10^158: 144/132 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 The second value is the cofactor size. Here's a size sorted listing of the above: Code: 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: Code: 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 } 15^133: Prime - GDB 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 Last fiddled with by EdH on 2022-07-06 at 12:40 Reason: Updates
 2022-03-16, 23:55 #2 RichD     Sep 2008 Kansas E0F16 Posts 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
 2022-03-17, 00:20 #3 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 17×271 Posts 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.
 2022-03-17, 02:35 #4 VBCurtis     "Curtis" Feb 2005 Riverside, CA 14D716 Posts I'll help with administration on this thread- updating post 1 with reservations, etc.
 2022-03-17, 12:32 #5 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 1,049 Posts 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
 2022-03-17, 14:51 #7 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 1,049 Posts 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.
2022-03-17, 15:43   #8
EdH

"Ed Hall"
Dec 2009

17·271 Posts

Quote:
 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.

 2022-03-17, 16:36 #9 RichD     Sep 2008 Kansas 59×61 Posts 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.
 2022-03-17, 18:44 #10 garambois     "Garambois Jean-Luc" Oct 2011 France 32×97 Posts 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.
 2022-03-17, 22:24 #11 RichD     Sep 2008 Kansas 59×61 Posts 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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