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 2019-10-01, 22:37 #210 garambois     "Garambois Jean-Luc" Oct 2011 France 24·43 Posts OK, LaurV, all right ! Perfect ! I'm waiting for your signal.
 2019-10-16, 00:31 #211 PFPoitras   "Patrick Poitras" Oct 2019 5×11 Posts Hello everyone. I'm new to the forum, but I've been working on some powers of integers, for integers that are fairly big. I'm doing powers of 385 (5*7*11) and 1155 (3*5*7*11), for i=1..50, I've got all of them to 90 digits or more, and am uploading them to factordb right now. I am progressively ramping up the maximum number of digits until I have them all to 100. Note that some of the powers are themselves larger than 100. I have not decided the course of action on those. How do I provide the data for everyone to peruse? I figure it can be grabbed from factordb, but for merges and stuff, how do I find which sequence it merged into?
 2019-10-17, 05:48 #212 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 22·11·223 Posts Welcome to the fray. Jean Luc may add 385 to the page linked in the first post of this thread. It should be the easiest way. Then anybody can follow your progress if he/she wants, and eventually spot mergers. If you work in the 90-100 digits, than a good indicator is the fact that your sequence magically jumps to over 100 or 120 digits. That means it merged with something else, and the most of "interesting" stuff is worked to 120 digits or so. Also, to have at least "some" probability to merge, your sequence needs to drop to low digit values (there are less small numbers than big numbers, at big numbers the probability to merge decreases to null). Last fiddled with by LaurV on 2019-10-17 at 05:53
2019-10-17, 14:20   #213
PFPoitras

"Patrick Poitras"
Oct 2019

5×11 Posts

Quote:
 Originally Posted by LaurV Welcome to the fray. Jean Luc may add 385 to the page linked in the first post of this thread. It should be the easiest way. Then anybody can follow your progress if he/she wants, and eventually spot mergers. If you work in the 90-100 digits, than a good indicator is the fact that your sequence magically jumps to over 100 or 120 digits. That means it merged with something else, and the most of "interesting" stuff is worked to 120 digits or so. Also, to have at least "some" probability to merge, your sequence needs to drop to low digit values (there are less small numbers than big numbers, at big numbers the probability to merge decreases to null).
Yeah I've already seen 385^4 jump to 143 digits on factordb,and 385^6 has 174, so they both merge somewhere upstream.

I've started working on a separate method for detecting mergers and keeping track of them across a compressed version of the factordb database. I think that might be useful for higher sequences, or if there aren't many merges up that high, it will at least make some nice graphs.

Last fiddled with by PFPoitras on 2019-10-17 at 14:22

 2019-10-17, 16:46 #214 garambois     "Garambois Jean-Luc" Oct 2011 France 24×43 Posts PFPoitras, I will indeed update the page in a few days and add bases 385 and 1155 for i from 1 to 50, as you ask. I suppose you want to book these two bases? To detect mergers, see here : https://www.mersenneforum.org/showthread.php?t=24423 For example, on factordb, you enter 385^4 and you copy the last term of the sequence which has 80 digits. It is 8276642735222359406410880925543291758092860223240575684888888809629485391239674704. Then you go to this page : http://www.aliquotes.com/OE_3000000_C80.txt And on this page, you use the "search" function and paste this 80-digit number. You immediately find that 385^4 merges with the sequence 903872. You still have to find out which index the merging is at and report it to me ! That's the sportiest part ! We find that the merging takes place at index 403 for the sequence 385^4 and at index 5 for the sequence 903872. This is noted as follows : 385^4:i403=903872:i5. I'll let you do the exercise again with 385^6 ! ;-)
 2019-10-18, 16:09 #215 PFPoitras   "Patrick Poitras" Oct 2019 5·11 Posts I've been working on the 385 and 1155 sequences for a bit now, so I can reserve the exponents up to N^50 for the time being and will likely release a bunch of them soon. I have increased the number of digits for most of them to about 105-110, and am pushing them to 120. As for the merges: 385^6:i244 = 3876:i5 1155^4:i36 = 1290378:i273 1155^6:i113 = 25968:i11 (Can someone double check that I got this right) Last fiddled with by PFPoitras on 2019-10-18 at 16:09
 2019-10-20, 14:47 #216 garambois     "Garambois Jean-Luc" Oct 2011 France 2B016 Posts OK, page updated. Thanks to all ! PFP, thanks to you for your help ! I think you made a mistake. I found this 1155^6:i112 = 25968:i10 and not 1155^6:i113 = 25968:i11 Do you confirm this ?
 2019-10-22, 23:07 #217 PFPoitras   "Patrick Poitras" Oct 2019 5·11 Posts Yes, you're correct for the correction. I worked on the 385 sequence, mostly on getting the 385 series' odd exponents to terminate. 385^31, 385^33, 385^41, 385^43 all terminate in primes. I have moved the 1155 sequence up a bit, but have yet to submit all the numbers, as I only have access to it during weekends.
 2019-11-24, 18:15 #218 garambois     "Garambois Jean-Luc" Oct 2011 France 24×43 Posts Thanks to all. Page updated. My own calculations : Some aliquot sequences in base 7 at 120 digits or more.
 2019-11-29, 18:49 #219 garambois     "Garambois Jean-Luc" Oct 2011 France 68810 Posts I have read information on this forum about a possible loss of factordb data. It seems to me that most of the aliquot sequences starting on integer powers that we have calculated so far have been lost ! For example factordb no longer responds for 7^102 and many other integer powers. I hope there is a recent copy of the database somewhere ! Otherwise, years of calculation would be lost...
 2019-12-04, 09:14 #220 garambois     "Garambois Jean-Luc" Oct 2011 France 24·43 Posts Many thanks to Syd and his possible collaborators for the data recovery on factordb. I find all our aliquot sequences with all the calculations we had done. Many thanks also for correcting the errors reported on this page: https://www.mersenneforum.org/showth...t=19737&page=3 I'll wait another 2 or 3 weeks before updating, so as not to overload factordb.

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