[quote=kar_bon;178242]BTW: it would be helpful to insert the page-link to Frank's 100000<n<200000 there![/quote]

That's in the "useful links" thread.

i think, it's easier for 'newbies' to find those information in one place!

[quote=kar_bon;178245]i think, it's easier for 'newbies' to find those information in one place![/quote]

OK then, I'll add it...

[code] 4914 . 62026286949058835776972477934632990726236491215516878025994491183877597202771819354403462736539911737838 = 2 * 3^2 * 3445904830503268654276248774146277262568693956417604334777471732437644289042878853022414596474439540991
4915 . 72364001440568641739801224257071822513942573084769691030326906381190530069900455913470706525963230360850 = 2 * 3 * 5^2 * 61^2 * 71 * 1826548517 * 31536315989 * 31700865885093797628294449081522886163858946263122204168932852502367848026333[/code]

That's the second time... :ouch1:

[URL="http://factordb.com/search.php?query=&se=1&aq=199152&action=last&fr=&to="]199152[/URL]: line 4952, size 124, 2^3*3*7, C107

Yes, Karsten, it needs to be all in one page just like you have it. Good work! I was having a hard time telling what was reserved and what wasn't. In the mean time:

In addition to the above 5 numbers, I'm also reserving:
20088, 101706, 102168, and 103840.

I'm generally picking out the ones with the smallest current factor that needs to be found (usually <= 85). On all of the numbers, I'll go until I encounter a C100 or greater.

I also searched a 10th number: 102216. I progressed from i=795 up to i=800. At that point, I encountered exactly a C100...so 102216 is unreserved.

I'm unreserving 233320. I went from i=477 at 102 digits to i=496 at 108 digits. i=496 has a C101. The most remarkable thing about this one is that the graph has been in a consecutive upslope since i=214. I'm not sure how common it is to have 272 consecutive indexes increase but I haven't noticed many that were so consistently upward. 2^3*3 has been a factor the entire time. It's been 2^5*3*7 ever since i=437.

This should leave me with 8 numbers reserved.

I noticed that you uploaded the info. for 117348. Darn, I was having fun with it. lol I knew the info. could probably be uploaded from somewhere but I learned a fair amount about what causes the sequences to go up and down by running it manually from i=~1140 to ~1260 before you did the upload, which put it at i=1358. I'm now at i=1363 with msieve just about done running a C89.

About 20088, I know all of its info. is not uploaded but I have about caught it up to where your page states it is. I started it from i=328 (where it was at in DB) and it's currently at i=412. I only need to go to i=446 so don't mess with uploading the remaining few indexes for it.


Gary

[quote=gd_barnes;178394]I'm unreserving 233320. I went from i=477 at 102 digits to i=496 at 108 digits. i=496 has a C101. The most remarkable thing about this one is that the graph has been in a consecutive upslope since i=214. I'm not sure how common it is to have 272 consecutive indexes increase but I haven't noticed many that were so consistently upward. 2^3*3 has been a factor the entire time. It's been 2^5*3*7 ever since i=437.[/quote]
You've ran into what's called a driver. A list of drivers is available at [URL]http://www.mersennewiki.org/index.php/Aliquot_Sequences#Drivers_and_guides[/URL]. Drivers, guides, and the downdriver tend to stick around for many lines. Note that all drivers and guides except the downdriver (2^1*3^0) will raise the sequence, some quicker than others. There are certain mathematical rules that determine when they leave (based, of course, on the factorization of the previous line...the only one I know is 2*p with p=1 mod 4 loses the downdriver). How hard they are to lose varies as well.
Some sequences will get and lose drivers and downdrivers repeatedly, making a large up and down, and extending the index to the thousands. Some, like 233320, get a driver that stays with it and consistently raises it through 100 or higher digits, like your case. If you were to examine a sequence that went up and down repeatedly, and separate it by the different driver/downdriver runs, it'd probably make yours there make a bit more sense.

Fascinating reading Tim. Thanks for the info. and link.

I've run into C>=100 and am now unreserving the following 2 numbers:

117348; taken from i=1358 to i=1365; has a C100.

233106; taken from i=1662 to i=1690; has a C102.

This should leave me with the following 6 numbers reserved:
20088, 101706, 102168, 103840, 117738, and 233324.


Of these, 233324 is the most interesting. It's been in a choppy stretch between 99 and 100 digits for the last 37 indexes (when it dropped its factor of 3) with a consistent factor of only 2^3.

I've been able to take 117738 the farthest; 40 indexes. It finally dropped its factor of 3 at 13 indexes ago. Although it's chopping up and down more now, it's at 112 digits and so I may have to unreserve it at any time now. But if the 3 stays away, it might be a good one for someone else with more dedicated resources to pick up at some point.


Gary

122688 acquired the downdriver at index 1133. DB updated.

[quote=Mini-Geek;178408]You've ran into what's called a driver. A list of drivers is available at [URL]http://www.mersennewiki.org/index.php/Aliquot_Sequences#Drivers_and_guides[/URL]. Drivers, guides, and the downdriver tend to stick around for many lines. Note that all drivers and guides except the downdriver (2^1*3^0) will raise the sequence, some quicker than others. There are certain mathematical rules that determine when they leave (based, of course, on the factorization of the previous line...the only one I know is 2*p with p=1 mod 4 loses the downdriver). How hard they are to lose varies as well.
Some sequences will get and lose drivers and downdrivers repeatedly, making a large up and down, and extending the index to the thousands. Some, like 233320, get a driver that stays with it and consistently raises it through 100 or higher digits, like your case. If you were to examine a sequence that went up and down repeatedly, and separate it by the different driver/downdriver runs, it'd probably make yours there make a bit more sense.[/quote]
The down driver is also lost if the factors are 2*n^2*p where n is a product of odd primes and p is a lone non-squared prime with p=1 mod 4.
I was noticing a 2* 11^2 * p for example for a downdriver loss. I notice this case wasn't mentioned in the article.

Does anyone know why there are only a few drivers if you don't include the perfect numbers? I would think there would be more than just 4.