Odds and ends....and class records

[Jatheski]

Originally Posted by Dubslow

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

He did it twice...

2340  i.750  sz.200   2^3 * 3^2 * 5 * 13 * 59 * 854029991 * C185
3270  i.714  sz.200   2^7 * 3 * 13 * 19 * 23 * 1446923 * 8768269 * C180

[unconnected]

Nice downdriver catch on 11040:

Checked 9579 170 (show) 7539036408...00<170> = 2^2 · 5^2 · 7^2 · 1538578858...13<167>
Checked 9580 171 (show) 1149164549...66<171> = 2 · 7^2 · 17 · 107 · 251 · 215023625077<12> · 1194437815...59<152>
Unchecked 9581 171 (show) 1002341817...74<171> = 2 · 7^2 · 17 · 41621 · 1445534102...09<163>

[Dubslow]

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

I ask because the recently terminated 498666 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]

Originally Posted by Dubslow

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

I ask because the recently terminated 498666 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.

Please see here.
Although the latest results 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 above and below mentioned web site page.

I am listing out aliquot sequences terminations in to the prime numbers to p ≥ 10⁶ 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 and series.

[LaurV]

Originally Posted by Dubslow

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

I ask because the recently terminated 498666 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.

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]

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

Vanity of vanities, all is vanity...

[Dubslow]

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

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>

[Batalov]

Here is what happens sometimes.

...
 2582 . c78 = 2 * 73984797699034119030153243403905276827050210732607559155739005238332911679729 
 2583 . c77 = 2^2 * 18496199424758529757538310850976319206762552683151889788934751309583227919933 
 2584 . c77 = 2 * 13 * 1487363090987141527397157421 * 1434872809225408937098565955809423560912617591911

Would it be nice if this happened more frequently?

[schickel]

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 1193892 I find this very interesting:

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

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]

Happy me thread:
Got DD for 865152 at 150 digits

[vasyannyasha]

Escape from 2⁶
3087 3883520684800021728793155600525505797862818464717560389541258977182719674383518775541911157072918588442565642944=2^6 * 60680010700000339512393056258211028091606538511211881086582171518479994912242480867842361829264352944415088171(110 digits)
3088 3822840674100021389280762544267294769771211926206348508454676805664239679471276294674068795243654235498150554900= 2^2 * 5^2 * 189817 * 982503047 · 12055362443482046791(20 digits) * 11554775476855370691465598351913(32 digits) * 1471551290954383777820887908367231538559068797(46 digits)