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-   -   Odds and ends....and class records (https://www.mersenneforum.org/showthread.php?t=11673)

 kar_bon 2009-07-21 17:26

there're 181 seqs <1M with factor-cubes with 3 or more(yes!!!) digits:

the highest:
853332:i246 2161
729000:i1173 953
758322:i1774 853
710430:i97 727
129792:i796 691
101820:i1029, 599
179082:i1244 467
759150:i254 349
104904:i1215 311
170196:i941 277
900648:i292 277
438360:i568 263
990504:i2441 227

addendum to squares: 84 seqs with 5 and more digits squared
seq 366600 is the only with two squared factors with 5 digits:
index 521 with 12583^2 and index 698 with 11677^2

 10metreh 2009-07-21 17:49

130396 kept a factor of 463 on two consecutive lines:

[code] 4957 . 207961754206463616793765484277213110316700348230083722919599534410914792242769427053913835672610213079911826 = 2 * 3 * 7 * 11 * [COLOR=red]463[/COLOR] * 2663 * 4019 * 5216329541 * 3013631473500903889 * 58589184986816593541 * 98627656344820166776497833078801051794543235077
4958 . 312036716334136823340977893106923114227632032874921556898327624777563236085802615865976096686699753441227374 = 2 * 3 * 11 * 13 * [COLOR=red]463[/COLOR] * 3617 * 5557 * 39079456455361764369665589516847777866075252947065734155131730765968715049059907798872958315049[/code]

 kar_bon 2009-07-21 18:20

here's another (choosen by random factor 797):

seq 11040:
[code]
3089 . 12563635146189922567676918255521152501614657939034576489878225480274222972082687585340536504 = 2^3 * 797 * 7561 * 20029 * 31334389 * 152340173 * 7112643748185163 * 383232004715380729172605955304225485941024022981
3090 . 11027035763528304587318683831357921028676237819707309270841087002896163582995304973630439496 = 2^3 * 797 * 835069183494260895441058999 * 2071037761339551333276963104943700514825471559385096671130379
[/code]

same in seq 021318: index 556 and 557.

those 2 only for seqs <30000!

another choice: factor 9973 (the last <10000):
found only a near miss in seq 34908: index 3998 and 4007!

interesting but hard to find, needs some programming to search for highest factor!

 gd_barnes 2009-07-26 21:58

Sequence 280686 has now eclipsed sequence 5352 as the longest known sequence that I am personally aware of that is ever-increasing. With small factors of only 2*3 that have never gone away, it has increased every time up to i=943 and is still only at 109 digits.

3^2 thru 3^6 have popped in from time to time but have quickly gone away. There was also a fairly long run of 2^2 thru 2^7 from i=406 to 495 but that also went away. It's been mostly 2*3.

I thought that 5352 was a slow increaser but it is currently at i=935 and 126 digits.

I'm guessing that others can quickly come up with an ever-increasing sequence that is at i>1000 but 280686 should be a good starting point for discussion about such a record. I'm not done with it yet but am getting close. Aliqueit.exe is currently working on a hard C99. I'll release it if I get a hard C>=100.

Gary

 gd_barnes 2009-07-27 23:11

I have now released 280686 at i=946; sz 109; C102; 2*3

To make it official: Sequence 280686 at i=946 is the longest-running ever-increasing sequence that I am aware of.

I'd like to challenge others to find a longer ever-increasing sequence or extend 280686 higher to perhaps >= 120 digits to see if it could be "cracked" or reach 1000 indexes. Maybe someone could come up with a list of sequences longer than 500 indexes that are ever-increasing.

Gary

 gd_barnes 2009-07-29 02:36

19278 will top 280686 as for the longest ever-increasing sequence sometime on Wednesday unless it acquires the downdriver in the next 2 indexes. :smile:

 gd_barnes 2009-07-30 08:19

19278 is pushing towards 1000 ever-increasing indexes and is maintaining its very slow creep upwards with the 2*3 small factors that occassionally morph into 2*3^2 or 2*3^3 before going back to 2*3 fairly quickly.

I'm currently at i=982 with a size of only 102 and am processing a tough C100.

 gd_barnes 2009-08-02 09:57

19278 finally ended it's ever-increasing run. After 1048 ever-increasing indexes, it lost it's factor of 3 at 1048 for a single index and went down before regaining the 3 right back at 1049 and starting its treck upward again. It's currently working at i=1049 at size 108 on a tough C100 (again).

Bummer!

Therefore, the unofficial records at the moment are:

Longest ever-increasing sequence: 280686 at 946.

Longest ever-increasing run anywhere within a sequence: 19278 at 1048.

That's something else people could check for anywhere in their sequences: Any run that is ever-increasing for longer than 1048 indexes even if there are some down runs elsewhere in the sequence.

Gary

 10metreh 2009-08-02 10:32

In fact, you escaped the 2 * 3 driver at line 1045. Good luck, it's now got a "blue" guide (as found in the reservations list).

 gd_barnes 2009-08-04 08:46

Even better: While maintaining the 2^2 guide, it has now dropped its factor of 3 again so has only been guided by 2^2 up until the current i=1065, when it went to 2^3 but still no factor of 3. Now it's on its way slowly down. Just gotta drop those one or two powers of 2 and I'll be rolling.

This one is really interesting so I've kept it going longer than usual. I've already solved two hard C100's (I usually stop there) and am currently working on a hard C102.

 10metreh 2009-08-04 09:37

[QUOTE=gd_barnes;183967]This one is really interesting so I've kept it going longer than usual. I've already solved two hard C100's (I usually stop there) and am currently working on a hard C102.[/QUOTE]

Out of interest, what is the largest GNFS you've done?

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