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2022-03-16, 21:33
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#1 |
"Ed Hall"
Dec 2009
Adirondack Mtns
126D16 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. 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:
38^108: 171/140 - VBcurtis 94^88: 174/140 - VBcurtis 99^87: 174/140 - VBcurtis 660^60: 170/140 - VBcurtis 770^60: 174/140 - VBcurtis 57^99: 174/141 - VBcurtis 510510^28: 130/124 - gd_barnes Code:
** 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:
20^110: Prime - GDB 20^112: Prime - GDB 20^114: Prime - GDB 21^113: Prime - GDB 22^112: Prime - GDB 23^111: Prime - GDB 24^108: Prime - GDB 26^106: Prime - GDB 26^108: Prime - GDB 28^102: Prime - GDB 28^104: Prime - GDB 28^106: Prime - GDB 28^112: Prime - GDB 29^109: Prime - GDB 30^102: Prime - GDB 35^107: Prime - GDB 37^109: Prime - GDB 42^98: Prime - GDB 42^100: Prime - GDB 44^94: Prime - GDB 46^92: Prime - GDB 47^95: Prime - GDB 54^88: Prime - GDB 55^97: Prime - GDB 59^93: Prime - GDB 59^95: Prime - GDB 59^97: Prime - GDB 67^95: Prime - GDB 69^83: Prime - GDB 75^87: Prime - GDB 78^76: Prime - GDB 78^80: Prime - GDB 87^77: Prime - GDB 88^78: Prime - GDB 89^93: Prime - GDB 90^80: Prime - GDB 93^85: Prime - GDB 94^72: Prime - EDH 94^76: Prime - GDB 102^2: Prime - A 102^4: Prime - A 102^6: Prime - A 102^8: Prime - A 102^10: Prime - A 102^12: Prime - A 102^14: Prime - A 102^16: Prime - A 102^18: Prime - A 102^20: Prime - A 102^22: Prime - A 102^24: Prime - A 102^26: Prime - A 102^28: Prime - A 102^30: Prime - A 102^32: Prime - A 102^34: Prime - A 102^36: Prime - A 102^38: Prime - A 102^40: Prime - A 102^42: Prime - A 102^44: Prime - A 102^46: Prime - A 102^48: Prime - A 102^50: Prime - A 102^52: Prime - A 102^54: Prime - GDB 102^56: Prime - GDB 102^58: Prime - GDB 102^60: Prime - GDB 102^62: Prime - GDB 102^64: Prime - GDB 102^66: Prime - GDB 102^68: Prime - GDB 102^70: Prime - GDB 102^72: Prime - GDB 102^74: Prime - GDB 102^76: Prime - GDB 102^78: Prime - GDB 102^80: Prime - GDB 104^2: Prime - A 104^4: Prime - A 104^6: Prime - A 104^8: Prime - A 104^10: Prime - A 104^12: Prime - A 104^14: Prime - A 104^16: Prime - A 104^18: Prime - A 104^20: Prime - A 104^22: Prime - A 104^24: Prime - A 104^26: Prime - A 104^28: Prime - A 104^30: Prime - A 104^32: Prime - A 104^34: Prime - A 104^36: Prime - A 104^38: Prime - A 104^40: Prime - A 104^42: Prime - A 104^44: Prime - A 104^46: Prime - A 104^48: Prime - A 104^50: Prime - A 104^52: Prime - RFD 104^54: Prime - RFD 104^56: Prime - RFD 104^58: Prime - GDB 104^60: Prime - GDB 104^62: Prime - GDB 104^64: Prime - GDB 104^66: Prime - GDB 104^68: Prime - GDB 104^70: Prime - GDB 104^72: Prime - GDB 104^74: Prime - GDB 104^76: Prime - GDB 104^80: Prime - GDB 105^75: Prime - GDB 113^89: Prime - GDB 120^2: Prime - A 120^4: Prime - A 120^6: Prime - A 120^8: Prime - A 120^10: Prime - A 120^12: Prime - A 120^14: Prime - A 120^16: Prime - A 120^18: Prime - A 120^20: Prime - A 120^22: Prime - A 120^24: Prime - A 120^26: Prime - A 120^28: Prime - A 120^30: Prime - A 120^32: Prime - A 120^34: Prime - A 120^36: Prime - A 120^38: Prime - A 120^40: Prime - A 120^42: Prime - A 120^44: Prime - A 120^46: Prime - A 120^48: Prime - GDB 120^50: Prime - A 120^52: Prime - GDB 120^54: Prime - GDB 120^56: Prime - GDB 120^58: Prime - GDB 120^60: Prime - GDB 120^62: Prime - GDB 120^64: Prime - GDB 120^66: Prime - GDB 120^68: Prime - GDB 120^70: Prime - GDB 120^72: Prime - GDB 120^74: Prime - A 120^76: Prime - GDB 137^79: Prime - GDB 163^69: Prime - GDB 167^75: Prime - GDB 167^77: Prime - GDB 173^71: Prime - GDB 179^71: Prime - GDB 191^65: Prime - GDB 199^65: Prime - GDB 227^65: Prime - GDB 227^71: Prime - GDB 229^65: Prime - RCH 239^71: Prime - GDB 239^73: Prime - GDB 241^63: Prime - GDB 251^1: Prime - A 251^3: Prime - A 251^5: Prime - A 251^7: Prime - A 251^9: Prime - RFD 251^11: Prime - RFD 251^13: Prime - A 251^15: Prime - RFD 251^17: Prime - A 251^19: Prime - RFD 251^21: Prime - RFD 251^23: Prime - RFD 251^25: Prime - RFD 251^27: Prime - RFD 251^29: Prime - RFD 251^31: Prime - RFD 251^33: Prime - RFD 251^35: Prime - RFD 251^37: Prime - RFD 251^39: Prime - RFD 251^41: Prime - RFD 251^43: Prime - RFD 251^45: Prime - RFD 251^47: Prime - RFD 251^49: Prime - RFD 251^51: Prime - GDB 251^53: Prime - RFD 251^55: Prime - GDB 251^57: Prime - GDB 251^59: Prime - GDB 251^61: Prime - A 251^63: Prime - GDB 251^65: Prime - GDB 251^67: Prime - GDB 251^69: Prime - GDB 257^1: Prime - A 257^3: Prime - A 257^5: Prime - A 257^7: Prime - A 257^9: Prime - A 257^11: Prime - RFD 257^13: Prime - RFD 257^15: Prime - RFD 257^17: Prime - RFD 257^19: Prime - RFD 257^21: Prime - RFD 257^23: Prime - A 257^25: Prime - RFD 257^27: Prime - RFD 257^29: Prime - RFD 257^31: Prime - RFD 257^33: Prime - RFD 257^35: Prime - RFD 257^37: Prime - RFD 257^39: Prime - RFD 257^41: Prime - RFD 257^43: Prime - RFD 257^45: Prime - RFD 257^47: Prime - RFD 257^49: Prime - RFD 257^51: Prime - GDB 257^53: Prime - RFD 257^55: Prime - GDB 257^57: Prime - GDB 257^59: Prime - A 257^61: Prime - A 257^63: Prime - GDB 257^67: Prime - GDB 263^1: Prime - A 263^3: Prime - A 263^5: Prime - A 263^7: Prime - A 263^9: Prime - RFD 263^11: Prime - RFD 263^13: Prime - RFD 263^15: Prime - RFD 263^17: Prime - RFD 263^19: Prime - A 263^21: Prime - RFD 263^23: Prime - RFD 263^25: Prime - RFD 263^27: Prime - RFD 263^29: Prime - RFD 263^31: Prime - RFD 263^33: Prime - RFD 263^35: Prime - RFD 263^37: Prime - RFD 263^39: Prime - RFD 263^41: Prime - RFD 263^43: Prime - RFD 263^45: Prime - RFD 263^47: Prime - RFD 263^49: Prime - RFD 263^51: Prime - GDB 263^53: Prime - GDB 263^55: Prime - GDB 263^57: Prime - GDB 263^59: Prime - GDB 263^61: Prime - GDB 263^63: Prime - GDB 263^65: Prime - GDB 263^67: Prime - GDB 263^69: Prime - GDB 269^1: Prime - A 269^3: Prime - A 269^5: Prime - A 269^7: Prime - A 269^9: Prime - RFD 269^11: Prime - RFD 269^13: Prime - RFD 269^15: Prime - RFD 269^17: Prime - RFD 269^19: Prime - RFD 269^21: Prime - RFD 269^23: Prime - RFD 269^25: Prime - RFD 269^27: Prime - RFD 269^29: Prime - RFD 269^31: Prime - RFD 269^33: Prime - RFD 269^35: Prime - RFD 269^37: Prime - RFD 269^39: Prime - RFD 269^41: Prime - RFD 269^43: Prime - RFD 269^45: Prime - RFD 269^47: Prime - RFD 269^49: Prime - RFD 269^51: Prime - GDB 269^53: Prime - GDB 269^55: Prime - GDB 269^57: Prime - GDB 269^59: Prime - GDB 269^61: Prime - GDB 269^63: Prime - GDB 271^1: Prime - A 271^3: Prime - A 271^5: Prime - A 271^7: Prime - A 271^9: Prime - RFD 271^11: Prime - RFD 271^13: Prime - RFD 271^15: Prime - RFD 271^17: Prime - RFD 271^19: Prime - RFD 271^21: Prime - RFD 271^23: Prime - RFD 271^25: Prime - RFD 271^27: Prime - RFD 271^29: Prime - RFD 271^31: Prime - RFD 271^33: Prime - RFD 271^35: Prime - RFD 271^37: Prime - RFD 271^39: Prime - RFD 271^41: Prime - A 271^43: Prime - RFD 271^45: Prime - RFD 271^47: Prime - RFD 271^49: Prime - GDB 271^51: Prime - GDB 271^53: Prime - GDB 271^55: Prime - GDB 271^57: Prime - GDB 271^59: Prime - GDB 271^61: Prime - GDB 271^63: Prime - GDB 277^1: Prime - A 277^3: Prime - A 277^5: Prime - A 277^7: Prime - A 277^9: Prime - RFD 277^11: Prime - RFD 277^13: Prime - RFD 277^15: Prime - RFD 277^17: Prime - RFD 277^19: Prime - A 277^21: Prime - RFD 277^23: Prime - RFD 277^25: Prime - RFD 277^27: Prime - RFD 277^29: Prime - RFD 277^31: Prime - RFD 277^33: Prime - RFD 277^35: Prime - RFD 277^37: Prime - RFD 277^39: Prime - RFD 277^41: Prime - RFD 277^43: Prime - RFD 277^45: Prime - RFD 277^47: Prime - RFD 277^49: Prime - GDB 277^51: Prime - GDB 277^53: Prime - GDB 277^55: Prime - GDB 277^57: Prime - GDB 277^59: Prime - GDB 277^61: Prime - GDB 277^63: Prime - GDB 277^65: Prime - GDB 277^67: Prime - GDB 281^1: Prime - A 281^3: Prime - A 281^5: Prime - A 281^7: Prime - A 281^9: Prime - A 281^11: Prime - RFD 281^13: Prime - RFD 281^15: Prime - RFD 281^17: Prime - RFD 281^19: Prime - RFD 281^21: Prime - RFD 281^23: Prime - RFD 281^25: Prime - RFD 281^27: Prime - RFD 281^29: Prime - RFD 281^31: Prime - RFD 281^33: Prime - RFD 281^35: Prime - RFD 281^37: Prime - RFD 281^39: Prime - RFD 281^41: Prime - RFD 281^43: Prime - RFD 281^45: Prime - RFD 281^47: Prime - RFD 281^49: Prime - RFD 281^51: Prime - RFD 281^53: Prime - RFD 281^55: Prime - GDB 281^57: Prime - GDB 281^59: Prime - GDB 281^61: Prime - GDB 281^63: Prime - GDB 281^65: Prime - GDB 281^67: Prime - GDB 281^69: Prime - GDB 283^1: Prime - A 283^3: Prime - A 283^5: Prime - A 283^7: Prime - A 283^9: Prime - A 283^11: Prime - A 283^13: Prime - A 283^15: Prime - A 283^17: Prime - A 283^19: Prime - A 283^21: Prime - A 283^23: Prime - RFD 283^25: Prime - RFD 283^27: Prime - RFD 283^29: Prime - A 283^31: Prime - A 283^33: Prime - RFD 283^35: Prime - RFD 283^37: Prime - RFD 283^39: Prime - RFD 283^41: Prime - RFD 283^43: Prime - RFD 283^45: Prime - RFD 283^47: Prime - RFD 283^49: Prime - RFD 283^51: Prime - GDB 283^53: Prime - GDB 283^55: Prime - GDB 283^57: Prime - GDB 283^59: Prime - GDB 283^61: Prime - GDB 288^61: Prime - GDB 293^1: Prime - A 293^3: Prime - A 293^5: Prime - A 293^7: Prime - A 293^9: Prime - RFD 293^11: Prime - RFD 293^13: Prime - RFD 293^15: Prime - RFD 293^17: Prime - RFD 293^19: Prime - RFD 293^21: Prime - RFD 293^23: Prime - RFD 293^25: Prime - RFD 293^27: Prime - RFD 293^29: Prime - RFD 293^31: Prime - A 293^33: Prime - RFD 293^35: Prime - RFD 293^37: Prime - RFD 293^39: Prime - RFD 293^41: Prime - RFD 293^43: Prime - RFD 293^45: Prime - RFD 293^47: Prime - RFD 293^49: Prime - GDB 293^51: Prime - GDB 293^53: Prime - GDB 293^55: Prime - GDB 293^57: Prime - GDB 293^59: Prime - GDB 293^61: Prime - GDB 293^63: Prime - GDB 293^65: Prime - EDH 306^58: Prime - GDB 306^60: Prime - GDB 306^64: Prime - GDB 338^63: Prime - GDB 392^61: Prime - GDB 392^62: Prime - GDB 648^54: Prime - GDB 882^51: Prime - GDB 1152^52: Prime - GDB 1184^46: Prime - GDB 1184^48: Prime - GDB 1184^50: Prime - GDB 1210^48: Prime - GDB 1210^50: Prime - GDB 1352^1: Prime - A 1352^2: Prime - A 1352^3: Prime - A 1352^4: Prime - A 1352^5: Prime - A 1352^6: Prime - A 1352^7: Prime - A 1352^8: Prime - A 1352^9: Prime - A 1352^10: Prime - A 1352^11: Prime - A 1352^12: Prime - A 1352^13: Prime - A 1352^14: Prime - A 1352^15: Prime - A 1352^16: Prime - RCH 1352^17: Prime - A 1352^18: Prime - RCH 1352^19: Prime - RCH 1352^20: Prime - RCH 1352^21: Prime - RCH 1352^22: Prime - RCH 1352^23: Prime - RCH 1352^24: Prime - RCH 1352^25: Prime - RCH 1352^26: Prime - RCH 1352^27: Prime - RCH 1352^28: Prime - RCH 1352^29: Prime - RCH 1352^30: Prime - RCH 1352^31: Prime - GDB 1352^32: Prime - GDB 1352^33: Prime - GDB 1352^34: Prime - GDB 1352^35: Prime - GDB 1352^36: Prime - GDB 1352^37: Prime - GDB 1352^38: Prime - GDB 1352^39: Prime - GDB 1352^40: Prime - GDB 1352^41: Prime - GDB 1352^42: Prime - GDB 1352^43: Prime - GDB 1352^44: Prime - GDB 1352^45: Prime - GDB 1352^46: Prime - GDB 1352^47: Prime - GDB 1352^48: Prime - GDB 1352^49: Prime - GDB 1352^50: Prime - EDH 1352^51: Prime - RCH 1352^53: Prime - GDB 14264^36: Prime - GDB 14288^36: Prime - GDB 14536^38: Prime - GDB 131071^1: Prime - A 131071^3: Prime - A 131071^5: Prime - A 131071^7: Prime - A 131071^9: Prime - A 131071^11: Prime - A 131071^13: Prime - A 131071^15: Prime - RCH 131071^17: Prime - A 131071^19: Prime - A 131071^21: Prime - RCH 131071^23: Prime - RCH 131071^25: Prime - RCH 131071^27: Prime - RCH 131071^29: Prime - RCH 131071^31: Prime - GDB 131071^37: Prime - GDB 524287^1: Prime - A 524287^3: Prime - A 524287^5: Prime - A 524287^7: Prime - A 524287^9: Prime - A 524287^11: Prime - A 524287^13: Prime - A 524287^15: Prime - GDB 524287^17: Prime - A 524287^19: Prime - GDB 524287^21: Prime - GDB 524287^23: Prime - A 524287^25: Prime - GDB 524287^27: Prime - GDB 524287^29: Prime - GDB 524287^31: Prime - GDB 9699690^22: Prime - GDB 2147483647^1: Prime - A 2147483647^3: Prime - A 2147483647^5: Prime - A 2147483647^7: Prime - A 2147483647^9: Prime - GDB 2147483647^11: Prime - GDB 2147483647^13: Prime - GDB 2147483647^15: Prime - GDB 2147483647^17: Prime - GDB 2147483647^19: Prime - GDB Last fiddled with by EdH on 2022-08-15 at 13:12 Reason: Updates |
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2022-03-16, 23:55
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#2 |
Sep 2008
Kansas
3×1,213 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 |
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2022-03-17, 00:20
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#3 |
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"Ed Hall"
Dec 2009
Adirondack Mtns
126D16 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. |
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2022-03-17, 02:35
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#4 |
"Curtis"
Feb 2005
Riverside, CA
538310 Posts |
I'll help with administration on this thread- updating post 1 with reservations, etc.
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2022-03-17, 12:32
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#5 |
"Oliver"
Sep 2017
Porta Westfalica, DE
100010000002 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 |
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2022-03-17, 14:07
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#6 |
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"Ed Hall"
Dec 2009
Adirondack Mtns
111558 Posts |
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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2022-03-17, 14:51
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#7 |
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"Oliver"
Sep 2017
Porta Westfalica, DE
26·17 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;
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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2022-03-17, 15:43
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#8 | |
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"Ed Hall"
Dec 2009
Adirondack Mtns
10010011011012 Posts |
Quote:
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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2022-03-17, 16:36
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#9 |
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Sep 2008
Kansas
3·1,213 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. |
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2022-03-17, 18:44
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#10 |
"Garambois Jean-Luc"
Oct 2011
France
32×103 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. |
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2022-03-17, 22:24
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#11 |
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Sep 2008
Kansas
70678 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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