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Old 2010-12-11, 03:57   #1
schickel
 
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Lightbulb Special project #2 - Driver escape attempt 2^3*3

OK, here's another one. These all have a slight chance of escape.

Since it turns out to be harder than anticipated to escape any of the drivers, this might not be worth a sticky thread any more....

Depending on how the large composite splits on these, there is a chance to escape from the driver:
Code:
  7392  1300. sz 165 2^3 * 3 * 13 - fivemack
125376  3504. sz 125 2^3 * 3 * 7
174984  2793. sz 125 2^3 * 3
207102  2866. sz 125 2^3 * 3 * 7
207360  1342. sz 115 2^3 * 3^2 - fivemack
208260  2420. sz 122 2^3 * 3 * 7^2 * 37 * 441281
218292  2963. sz 128 2^3 * 3^2
362640  4775. sz 126 2^3 * 3 * 11^2
390084  1006. sz 125 2^3 * 3
424428   793. sz 125 2^3 * 3^3
555912   812. sz 125 2^3 * 3 * 5^2 * 11 * 13
637236  1801. sz 125 2^3 * 3
917430  1143. sz 125 2^3 * 3
946776   514. sz 125 2^3 * 3^2

Last fiddled with by Mini-Geek on 2012-03-30 at 00:05 Reason: updating reservations
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Old 2010-12-11, 10:13   #2
henryzz
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reserving 532656
about to remove a couple that the database did

Last fiddled with by henryzz on 2010-12-11 at 10:15
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Old 2010-12-11, 12:58   #3
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Quote:
Originally Posted by schickel View Post
Mods: since these are longer lists, shall we delete the lines as we go?
Sounds like a plan to me.
from henryzz: me 2

Last fiddled with by henryzz on 2010-12-11 at 13:43
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Old 2010-12-11, 18:31   #4
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I'll take 925542 a little further
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Old 2010-12-12, 15:22   #5
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Quote:
Originally Posted by smh View Post
I'll take 925542 a little further
Her it is. i'll release this sequence.
Code:
550 . 32805115902336536005839595921149394269036607439622256941395432545090852308154235854244687545132205544 = 2^3 * 3^2 * 2898029 * 69416906723162592613278956745160785511931 * 2264858613082518205232153982405709304416457569206923 
551 . 56042103657623337349252434887821082443718558597412862029741454309627020964689014222206689133926707256 = 2^3 * 3^2 * 11 * 127 * 2777 * 5107 * 1114614649 * 106634898347 * 6047077224077460971463735839 * 54660571524065646006726292195794805778893 
552 . 110933393940508941687812612273771863974574378714349495477400860112498960704699082036766523568219852744 = 2^3 * 3^2 * 11 * 17 * 1847 * 11987 * 7896832871 * 173576260327 * 61287635256544142449366865996497 * 4429907498173355008301105340308206711 
553 . 236321088295776172554225769787667417847513611423658356576413474421399406539474393091984648030445793336 = 2^3 * 3^2 * 11 * 137 * 401347 * 378196126823225267631154527776855515686304793 * 14348933779811180985763224332053632856972595279 
554 . 466998567884497425035528949631222700501629062847253219365581895165464514256367262643791245312844497864 = 2^3 * 3^2 * 13463 * 624347 * 771640790479786742337930351179886807158171169909681360696724785457307437430098047912792917 
555 . 797885191527938691571769162003905977006566585958240912852980135293768654110519145695020653789476884856 = 2^3 * 3^2 * 109 * 343689911 * 23305780833968924341173154403989 * 12692610959783604464237541790291045299160510811870259888593 
556 . 1382879004199765892158655299976689286532517198278499847030221649193946636379577985313881348890155859144 = 2^3 * 3^2 * 71 * 4472297 * 266043450780354173 * 227357941570337078221666723630700836331333884444329333737102679964542436027 
557 . 2415169814320043671898347662398134470082793526695946301587788788438109809351786298527617298455349479096 = 2^3 * 3^2 * 610073417 * 7779516012441764601428873717 * 7067738862660897857505165094923687045268567677735604774290020587 
558 . 4125915110185207531989353717603767515589975354094187782550788757381741787325646383659873386418354818744 = 2^3 * 3^2 * 11 * 307 * 326562727 * 51962509526260772304180221826317766924950879889850081214445336208898038796133890159489113 
559 . 8103996165924948014918391149645550620920272373977292723848338873921265180742026343126502411075582375496 = 2^3 * 3^3 * 11 * 53 * 791257165301819 * 81331590462681477916174612743157231893993126925569492583422157783141529431600777703 
560 . 16916918240018319330394210705513391005361769838211632159696579552605988690046174318298526389642771288504 = 2^3 * 3^3 * 1289 * 16987 * 1827253 * 1957488464695523822054446894356457589103733164558764708377991275922051443660631318483611 
561 . 30113771250664140233737526483935575865780730049256104639892139116370489540720685568276682106696083687496 = 2^3 * 3^2 * 9969520742998500913147899053122351647450306139 * 41952550549596035591159295870908039599812504663380479187 
562 . 51444359219884572899301607743389942104042080508993259452264354475627023338288745883128295579551146104904 = 2^3 * 3^3 * 956383 * 21387861792163 * 388322741211276059 * 873741018938588767 * 34316994465693864997614355670434184964623671387 
563 . 91456788031304972465366934489355993394124515730776072094277011231766281540543194451320356726579978119096 = 2^3 * 3^3 * 61 * 1973 * 2914063888070361959 * 1207274991578557187140381527219458729181594043703857261315407721730233618652803 
564 . 166885416741676566422839454246737598112308309910072126924606644101728144224218725154425893377155773432904 = 2^3 * 3^3 * 11 * 863 * 62053 * 13019331359 * 5455762664989121 * 18465208799587727026535477160641162726437716620019297706007121895949 
565 . 339422121158451009859808544364750166148309670487658620195939370294306853255712115522509664163731983367096 = 2^3 * 3^3 * 151 * 10406613967330482274338010312875587630252320041932138220380775395336854711053228952738216340560828531 
566 . 609661072662088973559817996169503425730701917336552385502787345760414296392342364967215666095415578751304 = 2^3 * 3 * 2593 * 81439 * 1130911479026408160618653 * 106368653794408061310634215283949826630166314791250448715958091331338241 
567 . 915098126573512795204579006939566030377990233669981516120229938066019770940400163456003844164554553037496 = 2^3 * 3 * 149 * 72017233 * 324009946218166765817937734060499653 * 10966685344290262370882905518851829117226125556763140799429 
568 . 1388001217252412611826785201387658822346234985848370242241771128016676178243593967590885444498204652282504 = 2^3 * 3 * 11 * 31 * 502652977433 * 773742386658649 * 436073382051685087425259806308300217930171948573229635906834151163870440543 
569 . 2519568192029020603062219707975341531730025296978061606076501774486558223902722555651641504934684880133496 = 2^3 * 3 * 56509 * 23378488892769947582167 * 79465901929301408007110545024836746053755950830651140854500501560343616715743 
570 . 3779463755605867391728527161807706527465215869739551296248475239577430467895940908700026589522426314541704 = 2^3 * 3 * 2447 * 548032783636993703 * 117429830717338664203580180141859196224667958289533611827092863766047509501034520131 
571 . 5673056957229403748273381752076436580314107733594011439117419151641033688400747994179440322009115848002936 = 2^3 * 3 * 3697 * 4093 * 15031 * 1039266269810893754964323028267841610872347557595873887466583133158834832308748309099709720239 
572 . 8517831772564495142832145504521731174948823123658460104578516694626547331482634116826084002342775666006664 = 2^3 * 3 * 7 * 1248657471611041 * 2389577374285797242350242913 * 16992424895259870897637048183996598371156835359838766020271181 
573 . 15818830434762653326951020935441570896647866845930263163104120852544709990113946648220198471848582067089016 = 2^3 * 3^2 * 6965377 * 31542582441782032375098171952345250931555756354151284359578576317438680375236980967553671522271639 
574 . 27023841476856442247704307242189547655764037515170021963136656574252928133653998695254127729040609232495384 = 2^3 * 3^2 * 9199 * 672823 * 95112379996527920300027455240867 * 637582063687495624897584745991937215557105528249592897490227233 
575 . 46173794234209630199471069034955990147451602298048961958096538339855479799920591814170106622457924092176616 = 2^3 * 3 * 241 * 51599 * 88777097531260221330029 * 1742709713356489613380212955255966535282950236907838301556678946936763484069 
576 . 69741919047856149772550974711866857218161442306437355128784989070235081328601454355783146423492317135023384 = 2^3 * 3 * 19 * 239 * 257156221183553969623 * 6848078130580560537100523 * 363383670917317014026000790894489005613541188751476514169 
577 . 114557360532472808006322901637642524456990318633471176636221951261501640794828536401450939620765920601936616 = 2^3 * 3 * 19 * 29 * 37 * 109 * 557
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Old 2010-12-12, 15:25   #6
schickel
 
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Quote:
Originally Posted by smh View Post
Her it is. i'll release this sequence.
Code:
550 . 32805115902336536005839595921149394269036607439622256941395432545090852308154235854244687545132205544 = 2^3 * 3^2 * 2898029 * 69416906723162592613278956745160785511931 * 2264858613082518205232153982405709304416457569206923 

[ ... ]

577 . 114557360532472808006322901637642524456990318633471176636221951261501640794828536401450939620765920601936616 = 2^3 * 3 * 19 * 29 * 37 * 109 * 557
Boy, that sucker sure doesn't want to let go, does it?
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Old 2010-12-12, 19:02   #7
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Taking 127800, 993000 and 249912.
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Old 2010-12-13, 16:06   #8
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taking 896748 923286 (both have lost the special form; 923286 is 2^3*3^3 and 896748 is mibbling around with large powers of 2)
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Old 2010-12-15, 06:30   #9
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1st group:
A nice escape:
514746 592. sz 105 2^2 * 137


2nd group:
Escape from 2^3:
313710 1277. sz 105 2^4 * 3^3 * 59
616836 604. sz 103 2^4 * 3^2

I don't know if the ones for the 2nd group are considered "escapes" per se but they no longer fit the definition of this thread.

I'm not taking these any further.
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Old 2010-12-15, 12:17   #10
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Quote:
Originally Posted by gd_barnes View Post
2nd group:
Escape from 2^3:
313710 1277. sz 105 2^4 * 3^3 * 59
616836 604. sz 103 2^4 * 3^2

I don't know if the ones for the 2nd group are considered "escapes" per se but they no longer fit the definition of this thread.
2^3 * 3 is a driver, 2^4 * 3 is driverless (once the 3 goes away, will tend to push the sequence down; it might still be considered a guide, but I'm not sure), so I'd call that an escape.
Quote:
Originally Posted by schickel View Post
Mods: since these are longer lists, shall we delete the lines as we go?
Should this include escapes? Perhaps we should make a list of those, for people to take further? For now, I deleted Gary's 3 escapes and didn't relist them anywhere.

Last fiddled with by Mini-Geek on 2010-12-15 at 12:18
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Old 2010-12-15, 17:11   #11
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Quote:
Originally Posted by Mini-Geek View Post
2^3 * 3 is a driver, 2^4 * 3 is driverless (once the 3 goes away, will tend to push the sequence down; it might still be considered a guide, but I'm not sure), so I'd call that an escape.


Should this include escapes? Perhaps we should make a list of those, for people to take further? For now, I deleted Gary's 3 escapes and didn't relist them anywhere.
I think so. We might do a drive at some point soon that takes just driverless sequences higher. Sequences with 3s also quite possibly won't be taken so high. I would suggest once the two special projects are nearly finished.
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