20220727, 23:32  #606 
"Rich"
Aug 2002
Benicia, California
2^{2}×13×31 Posts 
1352^51 terminated by Ed and me.

20220728, 06:53  #607 
"Gary"
May 2007
Overland Park, KS
2×3^{2}×5×131 Posts 
As promised, below are updated lists of bases with the fewest and most sameparity sequences remaining. (Allparity sequences for doublesquare bases.) I included the recently initialized bases in this thread even though they are not on the pages yet under the assumption that they will be added in a manner similar to what was previously discussed.
For 1 remaining format is: Base (size/cofac/smallest fac) ********** Initialize size <= 180 digits: ********** Fewest: Code:
1 remain: 127 (173/152/113567) 167 (147/144/6469) 14536 (158/152/5) 9699690 (168/146/7) 200560490130 (160/126/3) 2 remain: 37, 42, 55, 59, 151, 239, 385, 552, 564, 660, 2310, 12496, 14316, 131071, 510510, 6469693230, 8589869056 Code:
11 remain: 200 10 remain: 28, 30 9 remain: 18, 78, 94, 882 8 remain: 40, 68, 88, 105 All sizes: ********** Fewest: Code:
1 remain: 14536 (158/152/5) 9699690 (168/146/7) 33550336* (181/143/3) 200560490130 (160/126/3) 7420738134810* (182/161/3) *  These bases are completed for <= 180 digits. 2 remain: 37, 42, 55, 59, 385, 552, 564, 660, 2310, 12496, 14316, 131071, 510510 Code:
14 remain: 94 12 remain: 78, 88, 92, 191, 200 11 remain: 72, 86, 87, 90, 91, 93, 95, 96, 99, 105, 199 Last fiddled with by gd_barnes on 20220728 at 06:58 
20220728, 07:32  #608  
"Gary"
May 2007
Overland Park, KS
2·3^{2}·5·131 Posts 
Quote:
One that you could add to the list is 14536^38. At 158/152 with a smallest factor of 5, it would be doable. It's not a prime base but is the easiest one remaining that would fully complete a base, regardless of size. Why would prime bases > 250 be too high? Prime bases have been shown to have sameparity sequences that terminate more easily. Quote:
Quote:
You mentioned about helping the project stay organized. A couple of things might help: (1) On the web page, separate the opposite and sameparity sequences with regard to the counts and percentages that are complete by base. That would tell us more accurately what remains on a base and how it is performing vs. its neighbors. (2) Have a standardization of the size that a base is tested to. This would give us more of an applestoapples comparison of everything that would make all of the count/percentage stats more accurate. It could even give us a heads up about anomalies in the performances of certain bases when compared to their neighbors that might lead JeanLuc onto something in the data harvest. Last fiddled with by gd_barnes on 20220728 at 07:43 

20220728, 10:21  #609 
"Gary"
May 2007
Overland Park, KS
2×3^{2}×5×131 Posts 
29^109 and 163^69 terminate

20220728, 12:54  #610  
"Ed Hall"
Dec 2009
Adirondack Mtns
12131_{8} Posts 
Quote:
Quote:


20220728, 13:10  #611 
"Ed Hall"
Dec 2009
Adirondack Mtns
5,209 Posts 
I think 180 is a bit too high for the current cutofff. I think 150 might be better for now. That way they can be brought down relatively quickly. I'm even reconsidering the one I just said I'd add (14536^38). That could easily turn into a few days to complete. I won't be doing much to help with initialization if I'm running other sequences. Let's revisit base completion after we do some other work.
Are we looking at 102 or 251 as a base to initialize? 
20220728, 13:54  #612 
"Ed Hall"
Dec 2009
Adirondack Mtns
5,209 Posts 
It looks like I'll be tied up for a bit. The list I mentioned will still be underway and I'm still thinking about 14536, but work as you would prefer and I'll try to catch up later.

20220728, 18:11  #613  
"Gary"
May 2007
Overland Park, KS
11790_{10} Posts 
Quote:
I was under the impression that we wanted to come as close as we can to fully completing bases; hence the 180digit cutoff. That said, I like your idea a whole lot better! Slowly working our way up a size list by base in this way seems a lot more doable. We could even go 150 until all complete, then 155, then 160, etc. It would give us plenty of interim base completions along the way that are not so difficult. At this point, if I made a list of sequences remaining by base that have a beginning start point of <= 150 digits, the list would likely have very little on it. I have lists of counts of bases/sequences separated with a start point of both <= 160 digits and 180 digits. I'll see what I can conger up for <= 150 digits. If it's almost nothing left, I can fairly quickly prepare one for <= 160 digits that could prove more useful. What about initializing base 120? I've seen that one mentioned a few times around here. I think I'd prefer that one instead of base 102 or 251. With lots of small factors in the base, it might have some interesting properties. Last fiddled with by gd_barnes on 20220728 at 18:41 

20220728, 22:56  #614 
"Gary"
May 2007
Overland Park, KS
2×3^{2}×5×131 Posts 
137^79, 167^77, and 392^62 terminate

20220729, 00:13  #615 
"Ed Hall"
Dec 2009
Adirondack Mtns
1010001011001_{2} Posts 
Base 120 was brought up by sweety a few posts back in the other thread. That exchange was the only mention I recall. It's certainly doable. RichD is working on 104 because I didn't know the status of 102. I'd like to fill that gap in also. Since 120 is of interest, let's initialize it to see what happens. Then, maybe we can fill in 102. Let's see what your next assessment shows. We may want to initialize the mixed parity before terminating the matched for some of these.

20220729, 00:20  #616 
"Gary"
May 2007
Overland Park, KS
2·3^{2}·5·131 Posts 
I added a column to my spreadsheet for starting size and got it populated for all sequences starting at <= 160 digits. That helps for what we are looking for. Below is what I came up with.
To the best of my knowledge, this is up to date as of this post. We have completed all sequences with a starting size at < 143 digits. Remaining for starting size <= 145 digits (last number is smallest factor): Code:
20^110: 144/140/3 78^76: 144/138/5 94^72: 142/142/3 306^58: 145/140/59 Code:
20^112: 144/134/3 20^114: 148/129/3 21^113: 150/147*/3 24^108: 150/144*/5 28^102: 148/142*/3 87^77: 144/141/3 94^76: 143/128/3 191^65: 144/139/3 199^65: 144/136/5 306^60: 148/139/7 1184^48: 148/145*/3 1210^48: 148/141*/3 14264^36: 144/131/3 14288^36: 148/141/7 Breaking it down in a count format by base like before for all <= 150 digits: 1 remaining: 21, 24, 28, 78, 87, 191, 199, 1184, 1210, 14264, 14288 2 remaining: 94, 306 3 remaining: 20 Last fiddled with by gd_barnes on 20220729 at 00:29 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Unexpected termination of PM1  Miszka  Software  22  20211119 21:36 
Easier pi(x) approximation  mathPuzzles  Math  8  20170504 10:58 
Would finding a definate Pi value easier if...  xtreme2k  Math  34  20130909 23:54 
Aliquot Termination Question  Largest Prime?  EdH  Aliquot Sequences  6  20100406 00:12 
A new termination below 100k  10metreh  Aliquot Sequences  0  20100311 18:24 