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 2022-03-16, 21:33 #1 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 10001100101102 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 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
 2022-03-16, 23:55 #2 RichD     Sep 2008 Kansas 67508 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 2·2,251 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 22×1,319 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 2·487 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 3CE16 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

10001100101102 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 23·5·89 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 11001001012 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 23·5·89 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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