Subproject #11: 2^2 * 3 - Lose the '3'

schickel · 2011-09-22, 10:47

This is a project suggested by 10metreh. He hopes we can achieve some terminations with this project.

The hope is that a sequence that currently has 2^2 * 3 as a guide will lose the 3, if the remaining composite factors "properly".

I pulled a status on these sequences right before posting but, as always, check the status of a sequence in the DB before starting any significant work....

[Note: Due to the sheer number of sequences that are currently 2^2 * 3, this message has been split....]

Sequences:

Code:

894702  1071. sz 112 2^2 * 3 * 11
668922  1469. sz 112 2^2 * 3 * 5
800010  1351. sz 112 2^2 * 3 * 5
596808  1007. sz 112 2^2 * 3 * 5
867228  1034. sz 112 2^2 * 3^2
638680   833. sz 112 2^2 * 3^2
738240  1698. sz 112 2^2 * 3^2 * 17
844758  1712. sz 112 2^2 * 3^2 * 5
630024  2457. sz 112 2^2 * 3^2 * 7 * 89459 * 138072719
293136   989. sz 113 2^2 * 3
369978  1188. sz 113 2^2 * 3
642000  1705. sz 113 2^2 * 3 * 1669
526752   618. sz 113 2^2 * 3 * 17
244872   844. sz 113 2^2 * 3 * 2437094789966273
966180  1880. sz 113 2^2 * 3 * 29
832314  2263. sz 113 2^2 * 3 * 5
932070  1072. sz 113 2^2 * 3 * 5
872784  1104. sz 113 2^2 * 3 * 5 * 11
746880   538. sz 113 2^2 * 3 * 5 * 11
734088  1169. sz 113 2^2 * 3 * 5^2
823116  1414. sz 113 2^2 * 3 * 53
665478   757. sz 113 2^2 * 3 * 577
592506  1114. sz 113 2^2 * 3 * 79
836694   894. sz 113 2^2 * 3^2 * 29
992970   999. sz 113 2^2 * 3^2 * 37
681500  1255. sz 113 2^2 * 3^2 * 5
704850  1590. sz 113 2^2 * 3^2 * 71
227200   781. sz 113 2^2 * 3^3
682380  1726. sz 113 2^2 * 3^3
777762  1384. sz 113 2^2 * 3^3
493992  1754. sz 113 2^2 * 3^3 * 5
385176  1097. sz 113 2^2 * 3^3 * 5
968484   970. sz 114 2^2 * 3
962232   828. sz 114 2^2 * 3
933240  1082. sz 114 2^2 * 3
891702  1122. sz 114 2^2 * 3
769068  1128. sz 114 2^2 * 3
601824  2081. sz 114 2^2 * 3
533160  1064. sz 114 2^2 * 3
564870   772. sz 114 2^2 * 3
239778  1486. sz 114 2^2 * 3
358506  1062. sz 114 2^2 * 3
656616  2093. sz 114 2^2 * 3 * 1097
106080   873. sz 114 2^2 * 3 * 137
559548  1250. sz 114 2^2 * 3 * 17 * 75883
699588  1280. sz 114 2^2 * 3 * 181
517392   878. sz 114 2^2 * 3 * 1823
323964  1940. sz 114 2^2 * 3 * 19
377160  1123. sz 114 2^2 * 3 * 281
946728  1014. sz 114 2^2 * 3 * 29
515220  1546. sz 114 2^2 * 3 * 317
712824   899. sz 114 2^2 * 3 * 3313
596032   546. sz 114 2^2 * 3 * 467 * 3582899
202776  1403. sz 114 2^2 * 3 * 47
384606  2109. sz 114 2^2 * 3 * 5
803616  1068. sz 114 2^2 * 3 * 5 * 103
425052  1059. sz 114 2^2 * 3 * 5 * 11
865032  1739. sz 114 2^2 * 3 * 5 * 13 * 37
870072  1052. sz 114 2^2 * 3 * 5 * 173 * 203989
871470   904. sz 114 2^2 * 3 * 5 * 19
863370   494. sz 114 2^2 * 3 * 5 * 383 * 9293 * 48673
429072  1087. sz 114 2^2 * 3 * 5^2 * 11
357408  1233. sz 114 2^2 * 3 * 5^3
960900  1599. sz 114 2^2 * 3 * 53
450570  2498. sz 114 2^2 * 3 * 543734960947
380610  2199. sz 114 2^2 * 3 * 607
636024   965. sz 114 2^2 * 3 * 71
556920  1027. sz 114 2^2 * 3 * 727
666384   978. sz 114 2^2 * 3^2
573648   530. sz 114 2^2 * 3^2
993438   510. sz 114 2^2 * 3^2 * 11 * 13
652296  1544. sz 114 2^2 * 3^2 * 11 * 19
940224  1739. sz 114 2^2 * 3^2 * 479
967024  1144. sz 114 2^2 * 3^2 * 5 * 17
779892   779. sz 114 2^2 * 3^3
933870   685. sz 114 2^2 * 3^3
442344  1132. sz 114 2^2 * 3^3
856548  1112. sz 114 2^2 * 3^3 * 11 * 37
582144  1095. sz 114 2^2 * 3^3 * 37
922158  1305. sz 115 2^2 * 3
862866   646. sz 115 2^2 * 3
274272   985. sz 115 2^2 * 3 * 283
894066  1194. sz 115 2^2 * 3 * 31 * 24373
192360   963. sz 115 2^2 * 3 * 37 * 53^2
680544  1275. sz 115 2^2 * 3 * 373
788106  1476. sz 115 2^2 * 3 * 439
377688  2005. sz 115 2^2 * 3 * 5
641520   934. sz 115 2^2 * 3 * 5 * 617
915384  1102. sz 115 2^2 * 3 * 79
216390   920. sz 115 2^2 * 3^2
269208  1199. sz 115 2^2 * 3^4 * 43
303756  2519. sz 116 2^2 * 3
749832   680. sz 116 2^2 * 3
865164  1065. sz 116 2^2 * 3
844536  1279. sz 116 2^2 * 3
687336  1137. sz 116 2^2 * 3
487656  2478. sz 116 2^2 * 3
475668   907. sz 116 2^2 * 3 * 11 * 1637
126756  1184. sz 116 2^2 * 3 * 11 * 433
287304  1485. sz 116 2^2 * 3 * 127
214728  1292. sz 116 2^2 * 3 * 13
394680  2382. sz 116 2^2 * 3 * 149 * 8712059
941850  2111. sz 116 2^2 * 3 * 17
270504  1912. sz 116 2^2 * 3 * 173
466656   799. sz 116 2^2 * 3 * 19 * 89
983328  1614. sz 116 2^2 * 3 * 239
492688  2368. sz 116 2^2 * 3 * 2591
333300  1237. sz 116 2^2 * 3 * 38923
863640  1048. sz 116 2^2 * 3 * 3943
929880  1075. sz 116 2^2 * 3 * 41
215088   912. sz 116 2^2 * 3 * 4421
950280  1250. sz 116 2^2 * 3 * 5
624798  1728. sz 116 2^2 * 3 * 5
746564   871. sz 116 2^2 * 3 * 5
478440   978. sz 116 2^2 * 3 * 5 * 47
443370  1530. sz 116 2^2 * 3 * 5 * 97 * 197
448476   851. sz 116 2^2 * 3 * 5^2 * 25121
376992   672. sz 116 2^2 * 3 * 59
758322  2239. sz 116 2^2 * 3 * 59 * 271
840012  1918. sz 116 2^2 * 3 * 709
426072  2703. sz 116 2^2 * 3 * 73 * 1151
324072  1027. sz 116 2^2 * 3^2
664356  2924. sz 116 2^2 * 3^2
407736   586. sz 116 2^2 * 3^2
180108   751. sz 116 2^2 * 3^2
103782   851. sz 116 2^2 * 3^2 * 11
850164  2307. sz 116 2^2 * 3^2 * 11 * 1289
967680  2008. sz 116 2^2 * 3^2 * 1571
582750  1396. sz 116 2^2 * 3^2 * 17 * 19
346200  1908. sz 116 2^2 * 3^2 * 17 * 29
421428   951. sz 116 2^2 * 3^2 * 2617
143676  1430. sz 116 2^2 * 3^2 * 283
296904   902. sz 116 2^2 * 3^2 * 37
183042   758. sz 116 2^2 * 3^2 * 467
649944  1514. sz 116 2^2 * 3^2 * 5
674912   407. sz 116 2^2 * 3^2 * 5
561000  2208. sz 116 2^2 * 3^2 * 5 * 13
190620  1468. sz 116 2^2 * 3^2 * 5^3 * 3408058099731294299
918054   835. sz 116 2^2 * 3^2 * 61
778300  1004. sz 116 2^2 * 3^2 * 991
338250  2866. sz 116 2^2 * 3^3
171462  1162. sz 116 2^2 * 3^3 * 115133
652386  1993. sz 116 2^2 * 3^3 * 13
971280  1235. sz 116 2^2 * 3^4
760000   832. sz 116 2^2 * 3^4 * 151
722142  1099. sz 116 2^2 * 3^5 * 11
834312  1311. sz 117 2^2 * 3
338040  1463. sz 117 2^2 * 3
711800  1277. sz 117 2^2 * 3 * 1073491
346980  2708. sz 117 2^2 * 3 * 1087
834756   645. sz 117 2^2 * 3 * 11 * 13 * 41
273552   898. sz 117 2^2 * 3 * 19 * 37 * 269
652068  1160. sz 117 2^2 * 3 * 23 * 853
245274  1424. sz 117 2^2 * 3 * 23333
852264  1187. sz 117 2^2 * 3 * 281
435504   702. sz 117 2^2 * 3 * 29 * 443
118230  1680. sz 117 2^2 * 3 * 333271
228228  1231. sz 117 2^2 * 3 * 3347
125016   980. sz 117 2^2 * 3 * 35839
288144  1343. sz 117 2^2 * 3 * 37 * 1393326973 * 13825514861
710610  1215. sz 117 2^2 * 3 * 41
441450  1068. sz 117 2^2 * 3 * 5

Last complete status update: 2012-Jun-08

PS. Check below for some discussion about what it takes to lose the 3.

Mini-Geek · 2011-09-22, 23:10

[Old message at the bottom...

]

Code:

112350  2272. sz 117 2^2 * 3 * 5 * 11 * 71
594288  1962. sz 117 2^2 * 3 * 5 * 19 * 23 * 137
408408   576. sz 117 2^2 * 3 * 5 * 20297
997944  2058. sz 117 2^2 * 3 * 5 * 229
799512   421. sz 117 2^2 * 3 * 5 * 59 * 1409
516588  1126. sz 117 2^2 * 3 * 5 * 593 * 12176539883962932799
753372  1284. sz 117 2^2 * 3 * 61
313704   573. sz 117 2^2 * 3 * 853999 * 2705291
958056   647. sz 117 2^2 * 3^2
357792  1206. sz 117 2^2 * 3^2 * 111491
193320   986. sz 117 2^2 * 3^2 * 17
139056  2251. sz 117 2^2 * 3^2 * 44533
427704  1480. sz 117 2^2 * 3^2 * 5
559368  1873. sz 117 2^2 * 3^2 * 5 * 173
392340  1906. sz 117 2^2 * 3^2 * 5^4
477084   707. sz 117 2^2 * 3^3 * 19
574344   797. sz 117 2^2 * 3^3 * 5 * 103561
197310  1125. sz 117 2^2 * 3^3 * 5 * 2671
781302  2328. sz 117 2^2 * 3^3 * 5 * 9619
619800  1502. sz 117 2^2 * 3^4 * 5
353520  1009. sz 118 2^2 * 3
786720   977. sz 118 2^2 * 3
578760  1618. sz 118 2^2 * 3 * 101 * 110647 * 722321737
509832  1739. sz 118 2^2 * 3 * 31 * 42257
136192   622. sz 118 2^2 * 3 * 5 * 103
878752  1562. sz 118 2^2 * 3 * 5 * 7^2
893670  1174. sz 118 2^2 * 3 * 5146289
251580  1474. sz 118 2^2 * 3 * 67
233304   818. sz 118 2^2 * 3^2
927468  1292. sz 118 2^2 * 3^2
111426  1149. sz 118 2^2 * 3^2 * 11 * 13 * 6779
316960  1131. sz 118 2^2 * 3^2 * 29 * 467
768612  1943. sz 118 2^2 * 3^2 * 383 * 1933
547200  1441. sz 118 2^2 * 3^2 * 39317
708930  1343. sz 118 2^2 * 3^2 * 39461 * 7660223
474580  2321. sz 118 2^2 * 3^2 * 5 * 2377
799200   918. sz 118 2^2 * 3^2 * 5 * 71 * 1949
914760  2157. sz 118 2^2 * 3^2 * 5039
116040  1362. sz 118 2^2 * 3^3 * 19 * 29^2 * 53 * 1287989
922752   803. sz 118 2^2 * 3^3 * 5 * 13 * 47
753522  1597. sz 118 2^2 * 3^3 * 5 * 23 * 1223
531024  2662. sz 118 2^2 * 3^4 * 23
293496   857. sz 118 2^2 * 3^4 * 5
873528   561. sz 119 2^2 * 3 * 103
766560  1681. sz 119 2^2 * 3 * 11 * 17 * 47 * 331
787620   636. sz 119 2^2 * 3 * 19^2 * 71 * 2333
935008  1907. sz 119 2^2 * 3 * 2514737
533904   946. sz 119 2^2 * 3 * 41 * 769
394200  1372. sz 119 2^2 * 3 * 5^2 * 19
269688  2920. sz 119 2^2 * 3^2 * 13 * 71
838602   983. sz 120 2^2 * 3
643530   911. sz 120 2^2 * 3 * 1064685151
479136  2773. sz 120 2^2 * 3 * 11
558120  3407. sz 120 2^2 * 3 * 23 * 79
467016  4034. sz 120 2^2 * 3 * 281
557490  1239. sz 120 2^2 * 3 * 5
252588  1589. sz 120 2^2 * 3 * 5 * 103 * 2693 * 4856055876957941
308610  2389. sz 120 2^2 * 3 * 5 * 11 * 467
853740   551. sz 120 2^2 * 3 * 5 * 43
657816  1422. sz 120 2^2 * 3 * 653
277956   731. sz 120 2^2 * 3 * 7 * 13 * 643 * 6733
875520  1643. sz 120 2^2 * 3 * 7 * 71 * 257 * 997 * 6337
404868  1149. sz 120 2^2 * 3 * 800221
400158  1737. sz 120 2^2 * 3 * 911124659
623190  1551. sz 120 2^2 * 3^2 * 19 * 67
402780   439. sz 121 2^2 * 3
267102   654. sz 121 2^2 * 3 * 137
972720  1390. sz 121 2^2 * 3 * 1877 * 122029 * 504485371877
337008   592. sz 121 2^2 * 3 * 19 * 43
350994   959. sz 121 2^2 * 3 * 39610189
334548   809. sz 121 2^2 * 3 * 5 * 157
344136   889. sz 121 2^2 * 3^2
693812  1094. sz 121 2^2 * 3^2 * 19 * 77291
378642  1295. sz 121 2^2 * 3^2 * 5
227160  1294. sz 121 2^2 * 3^2 * 661
342216  1646. sz 121 2^2 * 3^5 * 2687
894456   441. sz 122 2^2 * 3 * 11
515064  1728. sz 122 2^2 * 3 * 11357029
201048   695. sz 122 2^2 * 3 * 13 * 412967
236840   722. sz 122 2^2 * 3 * 19
315780   405. sz 122 2^2 * 3 * 47 * 16573
438462   419. sz 122 2^2 * 3 * 5
230520   414. sz 122 2^2 * 3 * 5 * 29
716130  1911. sz 122 2^2 * 3 * 8200463933
448224   729. sz 122 2^2 * 3^2
497928  3332. sz 122 2^2 * 3^2
 79584  1451. sz 122 2^2 * 3^2 * 11 * 23
981960   512. sz 122 2^2 * 3^2 * 12497 * 843811
662850  3663. sz 122 2^2 * 3^2 * 13
175602   561. sz 122 2^2 * 3^3 * 41 * 313 * 3187 * 6353 * 11117 * 201511
122508  1838. sz 122 2^2 * 3^3 * 5009
911484   401. sz 123 2^2 * 3 * 10037
178002  2070. sz 123 2^2 * 3^3 * 5
 61116  1655. sz 124 2^2 * 3
767520  4433. sz 124 2^2 * 3 * 11 * 151
827880  1228. sz 124 2^2 * 3^2
985080   410. sz 125 2^2 * 3
494808   716. sz 125 2^2 * 3
919386  1065. sz 125 2^2 * 3 * 11
469812  3179. sz 125 2^2 * 3 * 1231
904188  2830. sz 125 2^2 * 3 * 17 * 107 * 9109
363126  1579. sz 125 2^2 * 3 * 19
938250  1967. sz 125 2^2 * 3 * 5 * 1013 * 30941
122688  1477. sz 125 2^2 * 3 * 5 * 181 * 300721
523044  1529. sz 125 2^2 * 3 * 5 * 58481 * 41557478047
462168   928. sz 125 2^2 * 3 * 5 * 59
795912  2455. sz 125 2^2 * 3 * 5 * 7 * 19^2 * 89 * 397
761516  1447. sz 125 2^2 * 3 * 5^2 * 11 * 673
996252  1758. sz 125 2^2 * 3 * 578861
336990  1354. sz 125 2^2 * 3^2 * 11 * 31019
980784  1188. sz 125 2^2 * 3^2 * 149 * 8218961
159846   857. sz 125 2^2 * 3^2 * 17 * 53 * 271 * 3529
170748  1565. sz 125 2^2 * 3^2 * 5 * 7 * 41 * 43 * 317 * 373
836244  1762. sz 125 2^2 * 3^2 * 7 * 31 * 2905087 * 3354133
116688  1237. sz 125 2^2 * 3^3
917790  2507. sz 125 2^2 * 3^3 * 5 * 7 * 342521
530640  3465. sz 126 2^2 * 3 * 149670900061
228150   881. sz 126 2^2 * 3^2 * 5 * 175753
509928  4524. sz 127 2^2 * 3
168912  2014. sz 127 2^2 * 3 * 47 * 2311
837480  1466. sz 127 2^2 * 3 * 47 * 6113 * 431567
511440   719. sz 127 2^2 * 3 * 5 * 89
161064  1786. sz 128 2^2 * 3 * 17 * 577
158814  3458. sz 130 2^2 * 3 * 17 * 3529
794184  1820. sz 130 2^2 * 3 * 5360837011597
129336  1923. sz 130 2^2 * 3^2 * 29 * 7949
102360   430. sz 130 2^2 * 3^3 * 109 * 131 * 194463079493
181650  1951. sz 131 2^2 * 3
259704  4605. sz 132 2^2 * 3 * 16607 * 22532987
381510   916. sz 132 2^2 * 3^2 * 5 * 683 * 737766131
643760  1373. sz 134 2^2 * 3 * 29^2 * 251
805686   472. sz 134 2^2 * 3 * 41
854418   404. sz 134 2^2 * 3 * 67 * 251 * 2809691
223692  1359. sz 135 2^2 * 3^2 * 491
715776  1941. sz 136 2^2 * 3 * 11 * 13 * 19
 20076  3403. sz 136 2^2 * 3 * 50828150957
 38880  1139. sz 138 2^2 * 3
425280   665. sz 138 2^2 * 3 * 61 * 787 * 82781
 84054  1099. sz 139 2^2 * 3 * 5
128136   499. sz 139 2^2 * 3 * 5 * 118860961
 52374  2535. sz 139 2^2 * 3^3 * 5
 56928  1003. sz 140 2^2 * 3 * 17 * 766169
611156  5703. sz 144 2^2 * 3^2 * 167 * 6047 * 7451
998088  1304. sz 145 2^2 * 3^2
 39060  1123. sz 147 2^2 * 3 * 17 * 29
940050  1624. sz 152 2^2 * 3^3 * 1163
890460   898. sz 156 2^2 * 3 * 53 * 103

Last complete update: 2012-Jun-08

Reserving 199710.
Are we deleting once reserved, or adding a reservation tag? For now, I'll add a reservation tag, as it's easier to delete than to recover the info.

schickel · 2011-09-23, 02:30

Quote:

Originally Posted by Mini-Geek

Reserving 199710.
Are we deleting once reserved, or adding a reservation tag? For now, I'll add a reservation tag, as it's easier to delete than to recover the info.

That'll work for now. We'll have to see how the project goes....

RobertS · 2011-09-23, 10:34

Reserving 321660

Mini-Geek · 2011-09-23, 11:25

Quote:

Originally Posted by schickel

PS. Clifford has mentioned the required form for a factorization to result in losing the 3, but I'm haven't been able to find that email yet....

On this sort of subject: My driver has become 2^2 * 3^3. Is this significantly worse to get out of than 2^2 * 3? I'm wondering if that's why only 2^2 * 3^1 is listed.

10metreh · 2011-09-23, 15:40

Quote:

Originally Posted by Mini-Geek

On this sort of subject: My driver has become 2^2 * 3^3. Is this significantly worse to get out of than 2^2 * 3? I'm wondering if that's why only 2^2 * 3^1 is listed.

I think it has the same conditions; it isn't included because we don't the top post to become huge.

schickel · 2011-09-23, 21:46

Quote:

Originally Posted by 10metreh

I think it has the same conditions; it isn't included because we don't the top post to become huge.

A quick count shows that there are >600 sequences with some combination of 2^2 * 3, either alone or with other factors, but without a 7.

This is the highest power of 3 right now:

Code:

940224  1734. sz 113 2^2 * 3^9

For those following along at home, I'll post an updated status file on everything open later this afternoon.....

Batalov · 2011-09-23, 23:02

I'll take 611156 (i4327), 960096 (i2655) and 378756 (i2911).

Mini-Geek · 2011-09-24, 02:59

Escape from 2^2*3 to 2^2 successful at 118 digits!

http://factordb.com/sequences.php?se=1&aq=199710
It's now on a slow downward-ish slide, hopefully it will become the downdriver!

Batalov · 2011-09-24, 03:32

Don't forget - 3 comes and goes... See for example 611156.

schickel · 2011-09-24, 03:40

Quote:

Originally Posted by schickel

For those following along at home, I'll post an updated status file on everything open later this afternoon.....

As promised, here is a current status file for everything.....I left it sorted by sequence this time.

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2011-09-23, 10:34	#4
RobertS Aug 2009 somewhere C5₁₆ Posts	Reserving 321660

2011-09-23, 23:02	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,257 Posts	I'll take 611156 (i4327), 960096 (i2655) and 378756 (i2911).

2011-09-24, 02:59	#9
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts	Escape from 2^2*3 to 2^2 successful at 118 digits! http://factordb.com/sequences.php?se=1&aq=199710 It's now on a slow downward-ish slide, hopefully it will become the downdriver!

2011-09-24, 03:32	#10
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2429₁₆ Posts	Don't forget - 3 comes and goes... See for example 611156.