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

 Dubslow 2012-11-16 05:16

[QUOTE=Batalov;318522]Interesting... ([URL="http://factordb.com/sequences.php?se=1&aq=701694&action=range&fr=1368&to=1369"]701694[/URL])
[CODE]1368 . 2635632963...60<120> = 2^6 * 5 * 127^2 * ...[/CODE]
Let's see if it will get lucky...[/QUOTE]

Is anyone specifically working on that number/sequence?

Has anyone ever escaped the D6 above 100 digits?

 fivemack 2012-11-16 10:58

[QUOTE=Dubslow;318525]Has anyone ever escaped the D6 above 100 digits?[/QUOTE]

Yes; 19494 loses 2^6*127 between iterations 1527 and 1529, at 120 digits.

966180 loses 2^6*127 between iterations 2667 and 2669, at 107 digits

 fivemack 2012-11-29 18:11

Woah!

[url]http://www.factordb.com/sequences.php?se=1&aq=967680&action=range&fr=2244&to=2246[/url]

[code]

2176...=2^3*351761333792801269*25356551767842855735377*3050768335867988943102114407401134146256546294637884878439784097681804298170079324983823302833
1904...=2^18*23*31592049788968711916177574027287172876807461062046384435626327044988312164831828232373474413053383283349194768155648600900453389
^^^^
2070...=2^4*7*13*1249*250867*1105339387*410575613031300368528610633240316067333040739426517304279238611570239780248119375461533099612652475877729165957777
[/code]

 Batalov 2012-12-01 20:53

1 Attachment(s)
[URL="http://factordb.com/aliquot.php?type=1&aq=256950"]Lovely[/URL]

 LaurV 2012-12-04 19:54

[URL="http://factorization.ath.cx/sequences.php?se=1&aq=865152&action=range&fr=2850&to=2870"]This babe[/URL] is now in "let's accumulate twos and threes" phase... Soon it will look like Mrs LaurV's class... (she is teaching nursery, twos and threes, a herd of screaming and yelling funny little enemies running in all directions in the same time, like in cartoons)

 henryzz 2012-12-04 21:42

[QUOTE=LaurV;320489][URL="http://factorization.ath.cx/sequences.php?se=1&aq=865152&action=range&fr=2850&to=2870"]This babe[/URL] is now in "let's accumulate twos and threes" phase... Soon it will look like Mrs LaurV's class... (she is teaching nursery, twos and threes, a herd of screaming and yelling funny little enemies running in all directions in the same time, like in cartoons)[/QUOTE]

It also looks like it has frozen. The next iteration hasn't been added.

 Dubslow 2012-12-04 22:15

[QUOTE=henryzz;320497]It also looks like it has frozen. The next iteration hasn't been added.[/QUOTE]

That's because he chose show range. [URL="http://factorization.ath.cx/sequences.php?se=1&aq=865152&action=last20&fr=2850&to=2870"]Show last 20[/URL] works fine. :smile:

 henryzz 2012-12-04 22:52

[QUOTE=Dubslow;320500]That's because he chose show range. [URL="http://factorization.ath.cx/sequences.php?se=1&aq=865152&action=last20&fr=2850&to=2870"]Show last 20[/URL] works fine. :smile:[/QUOTE]

Whoops!:redface:

 Batalov 2013-01-12 08:59

Could have been a neat escape - [U][COLOR=#0066cc][URL="http://factordb.com/sequences.php?se=1&aq=556260&action=range&fr=1079&to=1079"]556260:i1079[/URL][/COLOR][/U]

 fivemack 2013-09-01 07:04

Getting a down-driver at 146 digits (300744:1976) is probably still worth the bother of a post

 schickel 2013-09-07 01:38

[QUOTE=fivemack;351546]Getting a down-driver at 146 digits (300744:1976) is probably still worth the bother of a post[/QUOTE]I think it's worth the bother. It's also worth pointing out that you're poised to reach 190 digits on the next line for 3270:[code] 3270 681. sz 189 2^5 * 3 * 7 * 173[/code]....and the remaining compsosite for that line is way easier than the remaining composite for 2340! :cool:

 fivemack 2013-09-07 08:53

The remaining composite for 2340 turned out to fall to yoyo@home within twelve hours, though line 723 at present has a C169.

 schickel 2013-10-16 10:25

[QUOTE=schickel;352258]It's also worth pointing out that you're poised to reach 190 digits on the next line for 3270:[code] 3270 681. sz 189 2^5 * 3 * 7 * 173[/code]....and the remaining compsosite for that line is way easier than the remaining composite for 2340! :cool:[/QUOTE][code] 3270 685. sz [COLOR="Red"][SIZE="4"][B]191[/B][/SIZE][/COLOR] 2^5 * 3 * 7 * 13 * 31 * 18367 * 122033 * 499361 * 1482193 * 18966336778806232276490656049667197[/code]....and it's another easy composite on the current line!
:party:

 schickel 2013-10-26 03:05

Looks like 4788 moved back into the "interesting" column. Just 2 lines after resisting with a c166 at i5159, it managed an escape from the 2^4 * 31 driver:[code]5161 . c178 = 2^4 * 3 * [COLOR="Green"]31^2[/COLOR] * [COLOR="Blue"]p173[/COLOR][/code]Unless fivemack has managed something better with his sequences, that probably marks the highest escape from this particular driver....

 schickel 2013-12-31 05:54

I reserved 700128 near the end August due to this:[code] 1882 . c122 = 2^7 * 3 * 27816090795033431421647 * 1573739082633338474019476144532863544084135415146570870950473219128280888685687864784951680801069
1883 . c122 = 2^9 * 3 * 11 * 31 * 739 * 174474631 * 412252805345226625546180653166679129602120931324735415704720724688694885689787111833973581300746154914457[/code]Over the weekend this happened:[code] 1982 . c157 = 2^9 * 3 * 11^2 * 31^2 * 3643 * 150001 * 189108569004053 * 69675109380045871029361348047346187133290234567730495195318011589440258052336901685633903077048928101441544013069281859233069
1983 . c157 = 2^7 * 3 * 11 * 31 * 1310279 * 76740098586190829 * 197944688524091695567064323419083487830421068960241620697916240444822809793706463342125136185194531401652932921754477782125734801[/code]Several lines later at almost 2000 lines it's still alive with 2^7 * 3, so I'll keep running it until it hits a driver or gets too large for me....

 schickel 2014-02-04 09:51

1 Attachment(s)
Darn the luck! 689652 just picked up a 3 so it won't stay where it's at, but check out the graph for the last ~100 lines!

 LaurV 2014-02-04 12:04

The thees come and go... as long as no 7, everything is fine :smile:

 richs 2014-04-28 00:19

I got a down-driver at 147 digits (829332:3098) on 9 January 2014 and rode it down to 98 digits (829332:3315) today when the downdriver was lost. :sad:

 schickel 2014-06-02 07:10

Just realized no one else posted about this. 4788 is now the highest sequence computed so far [B]and[/B] is not driver controlled. It is at 195 digits, edging out 3270 by 2 digits:[code] 1074 2035. sz 169 2^3
1464 2352. sz 169 2^3 * 3^2
7890 1944. sz 170 2^2 * 3^2 * 7 * 1060075109 * 681364910939
19560 486. sz 170 2^3 * 3 * 5 * 7 * 59 * 4520183
363270 1779. sz 170 2^3 * 5 * 11 * 547
7392 1328. sz 172 2^3 * 3 * 7^2
3906 1955. sz 173 2^2 * 3 * 7 * 11 * 1297 * 1553 * 271013
9708 1033. sz 173 2^2 * 3 * 7 * 17 * 877 * 6883
5400 3117. sz 174 2^2 * 3^2 * 7 * 15733 * 20143 * 1243481
1734 2602. sz 174 2^5 * 3 * 1409
564 3373. sz 175 2^2 * 3^2 * 7 * 13 * 71 * 4292236942619
3408 1506. sz 176 2 * 3^7 * 43 * 113 * 317 * 3361 * 8561627 * 1225035276902369264645249
8040 2468. sz 177 2^2 * 3^2 * 29 * 1223 * 181390031
3678 3114. sz 177 2^2 * 3^2 * 7 * 67 * 461 * 541 * 74509 * 216169733987
966 893. sz 178 2^2 * 3^2 * 5 * 83 * 2099
5748 1526. sz 178 2^2 * 7 * 71
162126 4283. sz 178 2^3 * 3 * 5 * 461
2514 3076. sz 178 2^4 * 3 * 101 * 349 * 366437 * 1745076913
552 1057. sz 179 2^2 * 3 * 71 * 145633
4380 2334. sz 179 2^3 * 3 * 41 * 5875978519
9588 2097. sz 179 2^3 * 3^2 * 7 * 41 * 143461
7044 3433. sz 180 2^9 * 3 * 7 * 11 * 31 * 3673
276 1771. sz 181 2 * 3^4 * 7 * 23 * 3748153 * 224875615513259 * 51402449163862115551039729
842592 8031. sz 181 2^3 * 3 * 5 * 37 * 73 * 11069
660 895. sz 183 2^3 * 3^2 * 5 * 3163 * 14159 * 32070039222359 * 81741146396847353333
8352 1764. sz 185 2^2 * 7 * 103 * 3917
3366 2124. sz 185 2^3 * 3^3 * 191
2340 732. sz 192 2^3 * 3^2 * 5 * 13 * 43 * 599 * 423587
3270 692. sz 193 2^5 * 3 * 7 * 181295646406163
4788 5232. sz 195 2^4 * 11 * 173 * 14369[/code]Also, you have to go all the way down to 179 digits to find a non-driver controlled sequence and all the way down to 169 digits to find one that is both non-driver controlled and does not have a 3 in the guide....

 henryzz 2014-06-02 10:50

It might be nice to try to be the first to 200 digits.

 schickel 2014-06-10 05:31

I just realized after checking Wolfgang's page that with the last termination we are one away from bringing the total open sequences below 1M down to 9200. If you check the earliest [URL="https://web.archive.org/web/20050619084649/http://www.aliquot.de/aliquote.htm"]capture[/URL] in the Wayback Machine (June 19, 2005) there were a total of 9474 open sequences below 1M then.

 unconnected 2014-06-10 08:09

[QUOTE=schickel;375484]I just realized after checking Wolfgang's page that with the last termination we are one away from bringing the total open sequences below 1M down to 9200. [/QUOTE]
I've 9197 in my list. Can you post yours for comparison?

 schickel 2014-06-10 08:42

[QUOTE=unconnected;375492]I've 9197 in my list. Can you post yours for comparison?[/QUOTE]See the current list [URL="http://www.mersenneforum.org/showpost.php?p=374556&postcount=14"]here[/URL]. It should be completely synced with Wolfgang's count.....

 Batalov 2014-11-16 23:17

167358 just lost its 28th downdriver. Well, I'll torture it some more (currently with "2 * 3", up from i2411 to i5984)

 Batalov 2015-01-05 17:59

Bah! Hambug!
My minions are drilling on three downdrivers at once (I saw two before, three is rather rare)
[CODE]399168 5/06:21 (c114) 2207 . 894688106.. = 2 * 101 * 8513 * 35027 * 118831655.. * 20224624
671020 5/05:48 (c123) 1982 . 929801650.. = 2 * 13^2 * 79 * 256471 * 1343059 * 200230087..
652524 5/04:30 (c126) 868 . 842875615.. = 2 * 13 * 797 * 111491 * 112691 * 103627483.. * 3
[/CODE]

 Dubslow 2016-01-10 01:04

I just discovered that fivemack is one C175 away from being the first to take an aliquot sequence over 200 digits.

[url]http://factordb.com/sequences.php?se=1&aq=2340&action=last20[/url]

The next term will have a log10 of 199.2866, meaning 200 digits starting with the following: 19,347,049,672,300,256...

 Jatheski 2016-02-10 12:06

[QUOTE=Dubslow;421733]I just discovered that fivemack is one C175 away from being the first to take an aliquot sequence over 200 digits.[/QUOTE]

He did it twice... :bow:
[CODE]
2340 i.750 sz.200 [COLOR=#000000]2^3[/COLOR] * [COLOR=#000000]3^2[/COLOR] * [COLOR=#000000]5[/COLOR] * [COLOR=#000000]13[/COLOR] * [COLOR=#000000]59[/COLOR] * [COLOR=#000000]854029991[/COLOR] * C185
3270 i.714 sz.[COLOR=#000000]200 2^7[/COLOR] * [COLOR=#000000]3[/COLOR] * [COLOR=#000000]13[/COLOR] * [COLOR=#000000]19[/COLOR] * [COLOR=#000000]23[/COLOR] * [COLOR=#000000]1446923[/COLOR] * [COLOR=#000000]8768269[/COLOR] * C180
[/CODE]

 unconnected 2016-05-24 11:11

Nice downdriver catch on 11040:

[CODE]Checked 9579 170 [URL="http://factordb.com/index.php?showid=1100000000839244265"](show)[/URL] [URL="http://factordb.com/index.php?id=1100000000839244265"][COLOR=#002099]7539036408...00[/COLOR][/URL]<170> = [URL="http://factordb.com/index.php?id=2"][COLOR=#000000]2^2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=5"][COLOR=#000000]5^2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=7"][COLOR=#000000]7^2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=1100000000839244266"][COLOR=#000000]1538578858...13[/COLOR][/URL]<167>
Checked 9580 171 [URL="http://factordb.com/index.php?showid=1100000000839244267"](show)[/URL] [URL="http://factordb.com/index.php?id=1100000000839244267"][COLOR=#002099]1149164549...66[/COLOR][/URL]<171> = [URL="http://factordb.com/index.php?id=2"][COLOR=#000000]2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=7"][COLOR=#000000]7^2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=17"][COLOR=#000000]17[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=107"][COLOR=#000000]107[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=251"][COLOR=#000000]251[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=215023625077"][COLOR=#000000]215023625077[/COLOR][/URL]<12> · [URL="http://factordb.com/index.php?id=1100000000839244270"][COLOR=#000000]1194437815...59[/COLOR][/URL]<152>
Unchecked 9581 171 [URL="http://factordb.com/index.php?showid=1100000000839244271"](show)[/URL] [URL="http://factordb.com/index.php?id=1100000000839244271"][COLOR=#002099]1002341817...74[/COLOR][/URL]<171> = [URL="http://factordb.com/index.php?id=2"][COLOR=#000000]2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=7"][COLOR=#000000]7^2[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=17"][COLOR=#000000]17[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=41621"][COLOR=#000000]41621[/COLOR][/URL] · [URL="http://factordb.com/index.php?id=1100000000839244273"][COLOR=#002099]1445534102...09[/COLOR][/URL]<163>[/CODE]

 Dubslow 2016-10-25 13:16

What are the largest known termination values (primes or say the smallest of a cycle)?

I ask because the [URL="http://factordb.com/sequences.php?se=1&aq=498666&action=last20"]recently terminated 498666[/URL] ends in a 7 digit prime after hitting upon 2^5 times a 6 digit perfect square, and that's surely a rarity among known terminations.

 Raman 2016-10-25 13:24

[QUOTE=Dubslow;445733]What are the largest known termination values (primes or say the smallest of a cycle)?

I ask because the [URL="http://factordb.com/sequences.php?se=1&aq=498666&action=last20"]recently terminated 498666[/URL] ends in a 7 digit prime after hitting upon 2^5 times a 6 digit perfect square, and that's surely a rarity among known terminations.[/QUOTE]

Although the [URL="http://mersenneforum.org/showthread.php?t=11837"]latest results[/URL] have not been updated there.

A lot of Aliquot sequences terminate in 321329 and for an other people's six digit Aliquot sequence terminations please see [URL="http://www.aliquot.de/tabellen/1-1m.txt"]above[/URL] and below [URL="http://www.aliquot.de/archiv/1m.zip"]mentioned[/URL] web site page.

I am listing out aliquot sequences terminations in to the prime numbers to p ≥ 10[sup]6[/sup] although the famous aliquot sequence with 17490 as the key number terminates in to the aliquot 4 cycle composite numbers to lowest possible p - lowest possible 1264460 / 1547860 / 1727636 / 1305184.

Aliquot Sequence 17130 terminates in 8128.
Aliquot Sequence 17490 terminates in 1264460 / 1547860 / 1727636 / 1305184.

Aliquot sequence 242190 terminates in 1544509.
Aliquot sequence 98880 terminates in 1846001.
Aliquot sequence 498666 terminates in 1909283.
Aliquot sequence 538830 terminates in 3275023.
Aliquot sequence 934332 terminates in 8177753.
Aliquot sequence 397416 terminates in 870451093.

Aliquot sequence [U]and series[/U].

 LaurV 2016-10-25 14:48

[QUOTE=Dubslow;445733]What are the largest known termination values (primes or say the smallest of a cycle)?

I ask because the [URL="http://factordb.com/sequences.php?se=1&aq=498666&action=last20"]recently terminated 498666[/URL] ends in a 7 digit prime after hitting upon 2^5 times a 6 digit perfect square, and that's surely a rarity among known terminations.[/QUOTE]
There are many "high" termination values. According with my DB, for example, 523712 terminates in 198198181; there are a lot of sequences terminating in 20422951 (the smallest of them is 14952), 150480 terminates in 233078257, 124830 ends in 301691801, 688728 ends in 34967089, 677784 ends in 44084477, 54880 ends in 870451093 (together with many-many-many others from which the longest is 397416), and 891210 ends in 4737865361. This is only from "skimming" those folders, but I think that the last one is the largest for sequences starting under 1M. About cycles, the largest seems to be 891144 ending in 445419376

 Batalov 2017-10-22 15:27

[CODE]1985 c140 4156037973...68<140> = 2^4 · 31 · 4146139 · 16939989491<11> · 64319841466292852978789<23> · 1854794805...53<98>
1986 c140 4156039978...32<140> = [COLOR=Blue]2^4 · 31^2 ·[/COLOR] 1236205993810645215409<22> · 1473749150061006628243449341<28> · 1483617453...53<88>
1987 c140 4164419091...08<140> = [COLOR=blue]2^3 · 31 ·[/COLOR] 653 · 107916617 · 19421463018180026967183469<26> · 1226928633...59<102>
1988 c140 3908090253...92<140> = [COLOR=blue]2^3 · [/COLOR]2568158253...13<69> · 1902185276...23<71>
1989 c140 3419578971...48<140> = 2^4 · 31 · 107 · 653 · 26876177 · 110809888669<12> · 1553152278134653635240518561263<31> · 2133211681...37<84>[/CODE]Vanity of vanities, all is vanity...

 Dubslow 2017-11-16 14:13

Here's a somewhat unlikely driver, in both its short duration and manner of being broken:

[code]Checked 782 114 (show) 1507502633...88<114> = 2^6 · 19 · 934863113741<12> · 1326100626...73<99>
Checked 783 114 (show) 1641392670...32<114> = 2^4 · 7 · 13 · 31 · 5522062593508203383<19> · 6585490017...39<90>
Checked 784 114 (show) 2398958517...08<114> = 2^4 · 7 · 31 · 43 · 1033 · 13581517 · 185105765810211478961380051549<30> · 6187368991...57<69>
Checked 785 114 (show) 3217326650...92<114> = 2^4 · 31 · 41 · 28559 · 48106410954829529<17> · 1151552307...77<89>
Checked 786 114 (show) 3374500220...08<114> = 2^4 · 31 · 1259 · 3919 · 13794311 · 229064016943<12> · 5914256515921845511737829212409<31> · 7378528314...09<55>
Checked 787 114 (show) 3381584804...92<114> = 2^4 · 31 · 97 · 467 · 661 · 6737524562882489<16> · 13699703360275019<17> · 4168819372849997059<19> · 5869380826673190551<19> · 10081650556881903041508451809236947<35>
Checked 788 114 (show) 3476299006...08<114> = 2^4 · 31 · 18094387 · 267923603686970090921704666384714549711<39> · 1445708042...89<66>
Checked 789 114 (show) 3476299390...72<114> = 2^4 · 31 · 167 · 1009 · 162048871 · 2970041571048799141831277387212860985990793063<46> · 8642100664...53<52>
Checked 790 114 (show) 3524863606...48<114> = 2^4 · 31 · 505825364329<12> · 13552895863583<14> · 35959685414474821256401<23> · 224707786080000186398514971777<30> · 12829033266149785940728260633105467<35>
Checked 791 114 (show) 3524863606...72<114> = 2^4 · 31 · 75868268557<11> · 68824718794957<14> · 1360993408...43<87>
Checked 792 114 (show) 3524863606...00<114> = 2^4 · 3^2 · 5^2 · 31^2 · 43 · 2369452313...93<106>
Checked 793 114 (show) 9408653377...64<114> = 2^3 · 3 · 23 · 31^2 · 71 · 28177613209<11> · 124269712748149790294802374249804841118570663<45> · 7134066563...41<52>[/code]

 Batalov 2017-11-24 22:58

Here is what happens sometimes.
[CODE]...
2582 . c78 = 2 * 73984797699034119030153243403905276827050210732607559155739005238332911679729
2583 . c77 = [COLOR=Red]2^2[/COLOR] * 18496199424758529757538310850976319206762552683151889788934751309583227919933
2584 . c77 = 2 * 13 * 1487363090987141527397157421 * 1434872809225408937098565955809423560912617591911
[/CODE]Would it be nice if this happened more frequently? :rolleyes:

 schickel 2017-12-02 05:37

I was looking at the sequences in the new region above 1e6 and saw that there a several in there with the full 2^9 * 3* 11 * 31 driver. Looking at [URL="http://factordb.com/sequences.php?se=1&aq=1193892&action=last20&fr=0&to=100"]1193892[/URL] I find this very interesting:[code]
750 . 63506507480139459657246685380957909805221952821374480050375059073856983012159222505329045974 = 2 * 3^4 * 223 * 444369576909999125236463629 * p61
751 . 79433234983047711456356882501371980892879030799553121287160513826947152547520593313528939946 = 2 * 3^4 * 2600957 * p84
752 . 98556119244529227487629768993367862843134460196486346149134997874944840878709473860923253434 = 2 * 3^2 * p91
753 . 114982139118617432068901397158929173316990203562567403840657497520768981025161052837743795712 = 2^9 * 3 * 11 * 31 * 10281373 * 17314848773 * p70
754 . 229964311807774799683353181195593676687649732708836344402658139003632440190845143232172454400 = 2^9 * 3 * 5^2 * 11 * 31 * 281 * 383 * 523777 * 388994540981 * 50870749670209884227766433 * p38[/code]I'll have to look back when I get a chance, but I wonder if any of the other 2^9 driver runs started that way; without looking, though, I bet there were tons of 2 * 3 escapes without getting the 2^9.

 LaurV 2017-12-15 09:12

Got DD for 865152 at 150 digits
:davar55:

 vasyannyasha 2018-01-12 21:09

Escape from [SIZE="4"]2[SUP]6[/SUP][/SIZE]
3087 3883520684800021728793155600525505797862818464717560389541258977182719674383518775541911157072918588442565642944=[COLOR="Red"]2^6[/COLOR] * 60680010700000339512393056258211028091606538511211881086582171518479994912242480867842361829264352944415088171(110 digits)
3088 3822840674100021389280762544267294769771211926206348508454676805664239679471276294674068795243654235498150554900= 2^2 * 5^2 * 189817 * 982503047 · 12055362443482046791(20 digits) * 11554775476855370691465598351913(32 digits) * 1471551290954383777820887908367231538559068797(46 digits)

 Dubslow 2018-01-12 21:19

That's not surprising or uncommon at all?

 Batalov 2018-03-15 23:21

Isn't it nice when things just work...

[URL="http://factordb.com/sequences.php?se=1&aq=1033878&action=range&fr=1880&to=1890"]1033878[/URL]

[CODE]...
1884 140 1210024075...00<140> = 2^6 · 5^2 · 127 · 136765630999<12> · 263151616937453<15> · 9255912103178722959401214503081<31> · 1787590630...19<78>
1885 140 1790835631...00<140> = [COLOR="red"]2^6 · 5^2 · 127^2[/COLOR] · 6939501952...21<132>
1886 140 2650709943...98<140> = [COLOR="Lime"][COLOR="Green"]2[/COLOR][/COLOR] · 127 · 1511 · 218422447 · 4466223823<10> · 6398431107...11<53> · 1106503459...37<64>[/CODE]

 Dubslow 2018-03-16 00:21

Now that's pretty unlikely :smile: what are the odds there? Perhaps 1/10^4, 1/10^5?

 Batalov 2018-08-30 03:13

Eeek,,,
[URL="http://factordb.com/sequences.php?se=1&aq=2005020&action=last20"]2005020[/URL] has length 15070.

 EdH 2018-08-30 16:24

[QUOTE=Batalov;494899]Eeek,,,
[URL="http://factordb.com/sequences.php?se=1&aq=2005020&action=last20"]2005020[/URL] has length 15070.[/QUOTE]
And most of those at <100 dd...

 LaurV 2018-09-21 05:59

Some nice and (kind of) rare [URL="http://factordb.com/sequences.php?se=1&aq=181428&action=range&fr=1027&to=1032"]break of D3[/URL] on seq 181428, at index 1028 (close to 160 digits), [U]without doubling of the 5[/U] - but doubling the 3, and getting a lucky C154 cofactor which split in two primes, 41*P153, haha, both being 1 (mod 4), so we went from 2^3*3^2*5 to 2^4*3^2*5^2*11^2, then 11^3, then it lost the 5's and all the small primes except a 3. We are struggling now with the C156 (still in ecm phase).

 LaurV 2018-10-19 03:44

Replying to myself again... it seems like nobody talks to me anymore :razz:

Mister 45792 (or is is Ms? Or Mrs, better!) gave use heart palpitations, when, after the [URL="http://factordb.com/aliquot.php?type=1&aq=45792&big=1"]Tibetan Plateau[/URL] where it didn't want to raise and it didn't want to fall for what it seemed to us to be a million terms, we were expecting to see the Everest, but actually it got the DD and it went down...

Then, it lost the DD exactly at index 1400 (!) and it went through a lot of changes from 2^2 to 2^3 to 2^4, even tapped into 2^9, but then it ended up with 2^3*5 guide. :sad:

We said "well, that was it".

But it still surprised us, when it lost the guide after just 4 steps, in quite an unexpected way. We knew from the past that you can lose the G3 without squaring the 5 (see also my former post about losing D3 in a similar way) but we didn't see it yet, in our reservations, and it was a time when we worked a lot of D3 sequences just because they used to "scary" the people off.. (see our former discussions with Frank, when we joined the aliquot club here on this forum).

(by the way, where is Frank? He didn't post for ages, and we didn't see him around too much for more than 6 months, did he win his lottery and forgot about us? :razz:)

Now, Mrs. 45792 has a [URL="http://factordb.com/sequences.php?se=1&aq=45792&action=range&fr=1398&to=1475"]2^3 with no tail[/URL], and we really love this, almost as much as we love the DD. That is because this is like a "second DD", (like the "deputy sheriff" hehe). Because 2^3 with no tail of 3 or 5 can not get a 3 or a 5 attached to it, until it gets rid of the third power of 2. And because of that, 2^3 goes usually down, not as fast as the DD, but yet, we love it more than 2^2, for example (where 3 and 5 can come and go as they please).

It could be quite nice to see a 5-starter termination, we didn't see one in ages...

 LaurV 2018-10-22 11:23

Let's bet if we get a [URL="http://factordb.com/aliquot.php?type=1&aq=1180272&big=1"]symmetric graph[/URL]... :razz:

 Drdmitry 2020-03-31 01:20

As far as I can see, there are only four aliquot sequences below 1000000 which never reached 140 digits:
15390 (reserved by yafu@home, last update 31.03.2020),
62820 (Batalov, 27.03.2019),
780576 (Batalov, 11.03.2019),

Among them, only the first one is actively developed. The other three were not continued for almost a year and look abandoned.

I think it would be great to reach a threshold of 140 digits for all sequences below 1e6. The last three sequences may either be unreserved, so someone else will be able to pick them up. Or Serge, you can continue with your two sequences till 140 digits. I suspect, that should not take too long.

 yoyo 2020-03-31 17:59

I'll take the 3 to yafu@home to proceed them a bit, at least to a C139.

 Drdmitry 2020-06-12 01:09

Finally, all aliquot sequences below 1e6 reach 140 digits at east once. :showoff:

It looks like the next milestone of 150 digits will take very long time.

 yoyo 2020-06-12 18:44

One of my goals is to run all sequences below 1e5 to a C149.

 Drdmitry 2020-07-27 12:00

There are only two aliquot sequences below 100000 which never reached 145 digits:
38052 (reserved by Clifford, last update 21.07.2019)
46758 (jacobs and Richard Guy, 25.12.2017)
Both of them look abandoned.

On top of those, there is only one aliquot sequence (95700, vacant) which reach 146 digits and 17 other sequences reach 147 digits.

I think it is possible to reach the milestone of 150 digits for all sequences below 10e5 in the near future.

 yoyo 2020-07-27 17:41

[QUOTE=Drdmitry;551725]There are only two aliquot sequences below 100000 which never reached 145 digits:
38052 (reserved by Clifford, last update 21.07.2019)
46758 (jacobs and Richard Guy, 25.12.2017)
Both of them look abandoned.
[/QUOTE]

I'll take both.

 Stargate38 2021-01-17 23:24

Is this a record or not?

I've never seen 2^2*3 last this long:

[URL="http://www.factordb.com/sequences.php?se=1&aq=46*10^28&action=range&fr=334&to=500"]Sequence 46*10^28[/URL]

It's usually <20 consecutive terms long, at least on the sequences I've run.

If anyone asks what so special about this number, it's from the hyperinflation of the Hungarian Pengő. There were 460000000000000000000000000000 pengős to a U.S. dollar at one point, then they replaced it with the forint. At that rate, a single atom of gold would be worth 189402135 pengős, given the price of gold back in 1946.

 LaurV 2021-01-18 03:10

[QUOTE=Stargate38;569549]Is this a record or not?[/QUOTE]
Yep. Record. The least valuable currency, ever. :razz:
(we guess. We never heard about pengos before, and we don't know if something worse than that ever happened to another currency, but even if it did, if what you say is true, than that pengo was a freaking low valuated currency!)
About the 2^2*3 guide, the 3 comes and goes, sometime with brothers too, and usually is not sticky, like you just said (that's why it is considered only a guide, not a driver), but there are rare cases when it is/was quite sticky too.

 Stargate38 2021-01-18 22:03

Update on that: It had 2^2*3 from i334 to i453, then it lost the 3 and mutated to a downdriver (2*2*3 at i453 -> 2^2*p at i454 -> 2^3*p at i455 -> 2 at i456).

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