20141119, 22:54  #12 
"Ed Hall"
Dec 2009
Adirondack Mtns
D11_{16} Posts 
Thanks. I had considered trying to construct some cycles per the described manner, but decided those constructable would have been, to any limit I might easily pursue. Now seeding, I hadn't considered. I may look more into that...

20141122, 04:07  #13  
"Ed Hall"
Dec 2009
Adirondack Mtns
3·5·223 Posts 
Quote:


20141122, 04:38  #14  
"Phil"
Sep 2002
Tracktown, U.S.A.
1117_{10} Posts 
Quote:
Do there exist sociable numbers of order three? They must be rare, as none have ever been found. 

20141122, 10:49  #15  
"Frank <^>"
Dec 2004
CDP Janesville
2×1,061 Posts 
Quote:
In fact, in the wrapup for the section on the 3cycle rule, he said that finding a 3cycle is likely to be as hard as finding an oddprefect number, in his opoinion. 

20141122, 16:11  #16 
"Ed Hall"
Dec 2009
Adirondack Mtns
3·5·223 Posts 
Thanks. Although I'm limiting my search to 4cycle (except for the one machine recently changed), they will record any three cycles, if one happens along.

20141123, 18:15  #17 
Nov 2011
Saint Maur, France
32_{16} Posts 
Ed, Congrats for your 4cycle.

20141124, 04:53  #18 
"Ed Hall"
Dec 2009
Adirondack Mtns
110100010001_{2} Posts 
Thanks Michel!

20141124, 15:02  #19 
"Ed Hall"
Dec 2009
Adirondack Mtns
3·5·223 Posts 
Wow, another one, already...
I restarted this project in May, after probably a year on and off of previous searching with no success up until recently, and now in less than a week of each other, two have appeared. Odds, anyone?
Code:
16687836720184 = 2^3 * 7 * 79 * 3772114991 19524467203016 = 2^3 * 23 * 439 * 2621 * 92221 18777616502584 = 2^3 * 23 * 113 * 3373 * 267749 18297447537416 = 2^3 * 71 * 179 * 179965453 Thanks to all who have assisted me in my endeavors... 
20141125, 17:38  #20 
Nov 2011
Saint Maur, France
2·5^{2} Posts 
Well done! I can imagine your thrill.

20141125, 17:54  #21 
Nov 2011
Saint Maur, France
32_{16} Posts 
Side notes.
djm.cc/sociable.txt: If you look closely at group 44, you'll see it is still the only group with powers of 2 that are all different; noticed by JM Pedersen when I wrote to him. OEIS: There are a few sequences related to 4sociable groups, you can see them by searching for A090615. Cheers. 
20141126, 04:34  #22  
"Ed Hall"
Dec 2009
Adirondack Mtns
3·5·223 Posts 
Quote:
Am I confusing something or did you mean powers of 3? I see they are 5 4 2 3. That is interesting. Thanks also for the OEIS link as well. 

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