20120324, 01:51  #12  
"Frank <^>"
Dec 2004
CDP Janesville
2122_{10} Posts 
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20120324, 02:02  #13  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
(Among other deficiencies is a complete lack of knowledge of factoring methods besides ECM, of which I only have a basic idea that it's similar to P1 and uses elliptic curves. I've gleaned that the first line of attack is ECM, but I'm not sure when to switch methods or what to use. You got any more links? :P) 

20160116, 23:33  #14 
Jan 2016
1_{8} Posts 
About the starting value of an Aliquot Sequence
I have question about the starting value of a aliquot sequence. OP said that an Aliquot sequences are generally referred to by their starting value, is there some numbers that start an Aliquot Sequence but is never in the middle of another aliquot sequence? how do you call those numbers? these numbers would be those that are not in the image of the aliquot sum function. Another related question, if such "patriarch numbers" exist (or what ever you call them), does every branch of an aliquot family tree have a "patriarch" that initiate that branch or its goes on and on indefinitely?
Thank you for your time =D 
20160117, 10:45  #15 
"Alexander"
Nov 2008
The Alamo City
2×379 Posts 
I will answer the first part of your question and try to come up with something for the second part. An untouchable number is a number that does not occur as the aliquot sum of any other number. There are infinitely many untouchable numbers, it is conjectured that only one is odd (5), and it is also believed that all but 2 and 5 are composite. This is a list of untouchable numbers below 700.
The second part is a little trickier. I would imagine that every full sequence branches from an untouchable number. (Could someone more knowledgeable confirm that?) But don't confuse that untouchable number with the starting value we use. We basically refer to sequences by their lowest value. For example, 564 is used as a starting value, but it is not an untouchable number as it is the aliquot sum of 563^2. Also, it is conjectured, but not yet proven, that all sequences terminate with a prime, perfect number, or aliquot cycle. There could be infinitely long sequences that never terminate. So that answer to both parts of your second question could be "yes." 
20160118, 13:58  #16  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
1011100011001_{2} Posts 
Quote:
I would guess that it would be much less likely to happen as numbers in general get bigger as you go upward in a sequence and smaller as you go down. Numbers are limited in how much they can go down so it is less likely to happen. We do get long sequences reaching smaller numbers than their starting value(i.e. merging with a smaller sequence). Need to get on with work now. Might think more later. Last fiddled with by henryzz on 20160118 at 13:58 

20210723, 07:14  #17 
Aug 2020
79*6581e4;3*2539e3
110001110_{2} Posts 
I noticed that some open end sequences (e.g. 26236) aren't in the blue page reservation table. Are those sequences that merge with others? I couldn't find this number in the terminations/mergers thread though.

20210723, 08:46  #18 
Nov 2011
2^{2}×5×13 Posts 
You can check that 26236:i3 coincides with 4800:i7.Therefore the open sequence which started from 26236 is the same as 4800.

20210723, 10:29  #19 
Aug 2020
79*6581e4;3*2539e3
2×199 Posts 
Where did you check it? I used the forum search and it came up empty.

20210727, 09:47  #20  
Nov 2011
2^{2}×5×13 Posts 
Quote:
Last fiddled with by Drdmitry on 20210727 at 09:47 

20210727, 12:51  #21  
"Ed Hall"
Dec 2009
Adirondack Mtns
2×1,999 Posts 
Quote:
Also, I thought you were already running my alimerge3 program.: https://www.mersenneforum.org/showpo...postcount=1201 Code:
$ ./alimerge3 26236 1 1 Running base 26236 from 1 through 1 . . . 26236^1:i3 merges with 4800:i7 Run took 15 seconds. 

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