20090721, 17:26  #56 
Mar 2006
Germany
2·11·131 Posts 
there're 181 seqs <1M with factorcubes 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 
20090721, 17:49  #57 
Nov 2008
2×3^{3}×43 Posts 
130396 kept a factor of 463 on two consecutive lines:
Code:
4957 . 207961754206463616793765484277213110316700348230083722919599534410914792242769427053913835672610213079911826 = 2 * 3 * 7 * 11 * 463 * 2663 * 4019 * 5216329541 * 3013631473500903889 * 58589184986816593541 * 98627656344820166776497833078801051794543235077 4958 . 312036716334136823340977893106923114227632032874921556898327624777563236085802615865976096686699753441227374 = 2 * 3 * 11 * 13 * 463 * 3617 * 5557 * 39079456455361764369665589516847777866075252947065734155131730765968715049059907798872958315049 
20090721, 18:20  #58 
Mar 2006
Germany
2·11·131 Posts 
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 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! 
20090726, 21:58  #59 
May 2007
Kansas; USA
3·3,449 Posts 
Sequence 280686 has now eclipsed sequence 5352 as the longest known sequence that I am personally aware of that is everincreasing. 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 everincreasing 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 Last fiddled with by gd_barnes on 20090726 at 21:59 
20090727, 23:11  #60 
May 2007
Kansas; USA
286B_{16} Posts 
I have now released 280686 at i=946; sz 109; C102; 2*3
To make it official: Sequence 280686 at i=946 is the longestrunning everincreasing sequence that I am aware of. I'd like to challenge others to find a longer everincreasing 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 everincreasing. Gary 
20090729, 02:36  #61 
May 2007
Kansas; USA
3×3,449 Posts 
19278 will top 280686 as for the longest everincreasing sequence sometime on Wednesday unless it acquires the downdriver in the next 2 indexes.

20090730, 08:19  #62 
May 2007
Kansas; USA
3×3,449 Posts 
19278 is pushing towards 1000 everincreasing 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. Last fiddled with by gd_barnes on 20090730 at 08:19 
20090802, 09:57  #63 
May 2007
Kansas; USA
24153_{8} Posts 
19278 finally ended it's everincreasing run. After 1048 everincreasing 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 everincreasing sequence: 280686 at 946. Longest everincreasing run anywhere within a sequence: 19278 at 1048. That's something else people could check for anywhere in their sequences: Any run that is everincreasing for longer than 1048 indexes even if there are some down runs elsewhere in the sequence. Gary Last fiddled with by gd_barnes on 20090802 at 10:04 
20090802, 10:32  #64 
Nov 2008
2322_{10} Posts 
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).

20090804, 08:46  #65 
May 2007
Kansas; USA
3·3,449 Posts 
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. Last fiddled with by gd_barnes on 20090804 at 08:47 
20090804, 09:37  #66 
Nov 2008
2×3^{3}×43 Posts 

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