20200831, 17:00  #529  
Oct 2011
351_{10} Posts 
Quote:
This time, I had about 3  4 hours of work to do the update ! It is likely that at the next update, I won't touch any more the bases where nobody reserved sequences. I will update these bases only once every 2 or 3 months. I think that the best thing for the moment is indeed to continue the calculations of the different bases that we have started. We will see how much new data we will have in a few weeks, months, or even a year. It all depends on how many volunteers are going to do the calculations. But everyone should be well aware that we may not find what we were looking for at the beginning. This project was born in the following way. When with friends we were looking at the infinite graph of the aliquot sequences (see the graph here), we wondered if among the sequences starting with integer powers of a prime number, there would be more that would end with the same prime number. For example, would sequences starting with 7^i (i=1, 2, 3...) end more often with the prime number 7 ? Today, we cannot answer this question. But we have found something else that we were not looking for at all at the beginning : the 133 conjectures of post #447. One never knows to which ideas the chance of reflections can lead us ? Maybe all the calculations we make will allow us to answer the original question. Maybe not ! Or maybe we'll again find something else that we didn't expect to find. But to find things, we have to look at the data and ask ourselves all sorts of questions. Anyone can do that... You have to be as creative as possible. But right now, I'm still waiting for an OpenEnd sequence in base 2, 18 or another base with an exponent that has the same parity as the base. 

20200831, 19:18  #530 
"Ed Hall"
Dec 2009
Adirondack Mtns
D34_{16} Posts 
@JeanLuc:
Thanks for all the work and explanation. I will possibly play with extending base 18, if RichD isn't working there anymore and then play randomly with the matched parity unreserved sequences in the various tables. But, as we study these, I'm beginning to get a different feeling for "open" sequences. Open really only means we haven't finished it. 2^552, after index 0, had 9 abundant indices. If, when it reached 168 digits, we stopped, it would have been considered "open" and would have met the search criteria. @RichD: Are you still doing work on base 18? 
20200831, 22:02  #531 
Sep 2008
Kansas
2×1,567 Posts 

20200831, 22:11  #532 
"Curtis"
Feb 2005
Riverside, CA
3·5·293 Posts 
This is the original hypothesis of the Aliquotsequence project that they all terminate, eventually. We keep cracking C190+ cofactors in hopes of breaking a driver and finding a new largestpeaksizethatstillterminates record.

20200901, 00:52  #533 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}×5×13^{2} Posts 
Thanks  I'll work there for a while, then.
When I first started playing with Aliquot sequences, I was in the GuySelfridge camp. But, since I've been working on this subproject, I'm swinging much more toward the CatalinDickson Conjecture. However, I have to keep in mind that we are really working on a tiny piece of the "big" picture by working with bases and powers. Then again, if all bases and powers terminate, then everything does, because all numbers can be bases. 
20200901, 16:44  #534  
Oct 2011
3^{3}·13 Posts 
Quote:
For 2^552, yes : 9 abundant indices. But not 9 even terms ! Just for information : I'm in the GuySelfridge camp and I think that one day we'll be able to build a number that we'll be sure is the start of an OpenEnd sequence that will grow endlessly... 

20200902, 00:56  #535  
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}·5·13^{2} Posts 
Quote:
I won't hold that against you. I might even move back that way myself. But, currently, we seem to be displaying a lot of evidence for terminations. 

20200902, 00:59  #536 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}×5×13^{2} Posts 
But, we need some new algorithms. My attention span is short. I can't reasonably factor a difficult c190.

20200902, 03:16  #537 
"Curtis"
Feb 2005
Riverside, CA
3·5·293 Posts 
That's what nfs@home is for. We merely need to ECMpretest and solve the matrix, a total of at most 20% of the sieve time.
Edit: Of course, all that does is delay the onset of notenoughattentionspan to ~C200. Last fiddled with by VBCurtis on 20200902 at 03:16 
20200902, 19:23  #538  
Oct 2011
15F_{16} Posts 
Quote:
In fact, I don't really know what we should consider an OpenEnd sequence. But I do make two observations : 1) In the main project, on the blue page, I've never seen an OpenEnd sequence that starts on an odd number. But maybe there is one and I don't know how to filter it ? 2) On all the aliquots sequences that start on integers from 1 to 10,000,000, thanks to my fundamental database, I know that the absolute record for a growth sequence with consecutive odd terms is held by the sequence that starts on the integer 2,551,185. And this number of growing consecutive terms is only 6, which is very little. (see here some other records) Having made these two observations, I tell myself that a sequence can only be OpenEnd with even terms for numbers of a few hundred digits that we work with. But maybe it should also be possible to have an OpenEnd sequence with huge odd terms. But discovering such odd OpenEnd sequences (if they exist) is far from being within our reach. 

20200906, 17:57  #539 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}·5·13^{2} Posts 
In case you do an update this weekend prior to my finishing 18^119, I have otherwise completed a new row for base 18, through 18^118 at present.
I am running 18^119 and hope to have it done soon. For now, I will not be extending the table further. 
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