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-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

garambois 2022-01-20 19:00

[QUOTE=EdH;598326]This was just too interesting to me not to share. Aliquot sequence 71^87 term 3 shed 74 digits in its single step to term 4. More like this would be nice.[/QUOTE]

This is indeed rare and worth noting !
I had fun a long time ago to "make" such strange aliquot sequences of which [URL="http://factordb.com/sequences.php?se=1&aq=149630548933897631212666947906203267592255231218283454607956855773953854358615791539862703269440864073736722944516666258662795314877330378839040266281998618263406853152253439332649464770129875952018446539257287284810296582829172060793796048749479171967404610278137743531971149710700641903411146036494585805109587178502632293249051602509426886972295062675401903392390994694645668951473125480523473840116458314978726814528688636742439642334770567122351179439251530822855480182718390076212234206826434577800477996951107153259277674147403179956100395392301573285636312357028069714998507372755029864110750348158315552442048552231849821111494022294869325803320134980274911239499735516753888825800536914962254988235304796452098869117749285079667385663723903015145909688554720581582619524326773951323547055832210937916096474474897746952310472696618766798879167458740821576599066217868763939419909216849255539123378331933017763101238907296429619957673479451002889682088451986894668538548370277499804057864344763404649938455326552512133957896454468215862173451643619511130828755367440458845645189914798544027674269732307846403005841327251397509337663412702901937794015707758185929527674836430482992606233067444837807460829303862409329398284320150205631739060228554840534843586112404269329795163378502751594933636283421108140184489075896958324102113283998063692980650702646000978106468755357199751531359344086777681847269282620105502946881642168187781666027487104220094403421285457763915092348330789675393758986904293364385285313757780584619260425156687466470410951429496109797255683067460339343631767542587227178489520664340700475044539139327350779183982664488107573844535846186720329521103907322461967989389990228837277864114375748458571526037921883895849670434416996586175469246637037727255826771628435101946859551754877137457709360326268675701425789008957519029160130015298165027025213372853729490475631827773513170597661748601750166508186470123002786831546051027391844267724026928815972545516493884454324905297015699149850324873739938025394413781542343584532420571640977235740657210215768621321135196042756225734707568752135694047660033652611574145140178349458163507466737029615898622062177464575852781522315963431272586007055517403280711236755874163459685159603908336490469412703509699402300334797857598312347685700448430107880768552376514661673907826774384410094620400380381822545219717880868432087289980815697451676637054173651143041777106763361008332595383282559682297501134380960817668408020500674812760097006444472778999002476602634329910206470935337753029058495718456491820409454397607387652362126706065731098991106761054278477888042822008591215993550061171642539464930158644329270313871982507242675204019863247323058908114602772135089064798381096423513471540694610561414281795333952666472887604826100063772868395916611277966816981964045719561000011414806203094756765910236327442411491877516715647719329197188806344225320800964629240809823932893116295590365005547297556010017141853493519327008319247058821827297190100534408019245602490212560595167878587375530044021303301514966857163711048430672804110796125447872013793758534153643026996609416212110917091217206265982125526630840621544455847939180083090635151921333454867691457480503869888071123233540272383300463476869271999148348605693537195317423380537026427073231791558183378314572647287492030594198989845758637297102144442073347059643750885521335544700642677116237530884175122859655362634093510453784503429605816342129692507158466937258481593048232672273273176862906774315591010855444342496177443020916638248805081693621385351241172747064945822424526859924948615028476517074637973462543570724982239057505948685448426046770449996850099131082876342453894153694607789553152139306254191180408240012930063113684477778606564671788220393956625450522004143545285648411622564988709136518122877591074985883154688355213932675813165770341310456809140296337292004569138749921630356070101742782409136365599109824358235226440496056480776809560490102157010589491771376432152487762936899075751204693698648045118497050228403003966233252419085880464203722916358528133354309985902114143944304650417271471191704273609283468726959876158033449166748778099932891196694411824745086478674689243923971732606993660969596873199050273148634342547582629488220535361936664483267225788697512468879162025582122251727051771875220246629080812447799720941927102144415484046681639633796148362360043444853688014495060688678216922190188773878287379550997793339954696700204509895053807358732669278818326225857027948511323653368024685394989469724515046124910462229157784625259630166688577711640103513954907170074999500797973494012301859729325857138825943359830417445677167164235899661503550017719989019398981750756654140525882466692084391556075562649946147274307816024317596292079444572823358377033777905006163868803723365654938580266375857408133957114318081516032613544414076399574507749505653631176679959206411376265267224910363734832217299031234543760163344081412945030068294038038534735714879887145120496681479101913284598283302379023181086139420345746579396800730205644031774543094468277504929568378042777469554137419373876443418097639743168565443594484510275711546806618210065947547158645404402087283471172846738444123711809522612430100829281018551996627433852127927395310704056289479642223216744960522115814869505078956213643321828360200621270073716741790192350437087516506462397653266627882263913477380258014863719444104413590938188224287747321987391816077847430002548880391390061011611119140596137751063010973737629841350470649597404671242010053820991304661992833432792194967631786937581924810637864734047899671665617289304797018773609866243334509145007249358713464031390307794962696243548100498345073465081397507124103526509690176715706479860993088490335936701239366173061735135998849228619868350104919384314582061646975346808959786549826374088579994487380912605900249322591911033754519695278781547752608863632996633746281879603058357327452724803276181415048005645931617091134567689057618058522792817391252153891945388265419223212627350603680664950375452015288606681565139978173089200107507366712195250759744146508224369683611073668131290946112621339743663578818886550099824331538339898224067211191849472520822545984110913092873024343752960360359889962016982356565075720498271882801402733192606180681431228484965522195714627898753077767431611261934070780345688929535295743586792473384615812929873802815202565243538616287742079493236126383926037437250114799849070787662749212768585719356160425400206759606384634934531103525864420775109439142795608600064603406546659565484874288317631530681161147311491558259998951863456892309236742643639634155158745824765558189275974949867841622157606118036325809511872849121460465691285380261405910932325228841062537722855607415637965032470371016433411395020365579016194169246794123221959025313527565794466675930723576143639161299922916118409945830233786813989230194836219936468177925639622283954886911780834316245285627584217918948361977380655456775536688433559503431972932467025829599914872751991889016816729807561406853222647922635915321649017068592493853129117572631558916794005405301282888619680008853528491291448853860614946438431000436845897095452736429393921385376859738907389114009779954780130115933124773956114549460824880850669162781653780128167087&action=last20&fr=0&to=100"]here is an example[/URL] !
We start with 7317 digit terms and divide the number of digits by two at each iteration.
I even think I could "make" some pretty funny aliquot sequences of similar types.
For example one that would start with a term of 8000 digits, and whose second term would have 7000 digits, and whose third term would have 6000 digits, ...

EdH 2022-01-20 23:45

[QUOTE=garambois;598428]This is indeed rare and worth noting !
I had fun a long time ago to "make" such strange aliquot sequences of which [URL="http://factordb.com/sequences.php?se=1&aq=149630548933897631212666947906203267592255231218283454607956855773953854358615791539862703269440864073736722944516666258662795314877330378839040266281998618263406853152253439332649464770129875952018446539257287284810296582829172060793796048749479171967404610278137743531971149710700641903411146036494585805109587178502632293249051602509426886972295062675401903392390994694645668951473125480523473840116458314978726814528688636742439642334770567122351179439251530822855480182718390076212234206826434577800477996951107153259277674147403179956100395392301573285636312357028069714998507372755029864110750348158315552442048552231849821111494022294869325803320134980274911239499735516753888825800536914962254988235304796452098869117749285079667385663723903015145909688554720581582619524326773951323547055832210937916096474474897746952310472696618766798879167458740821576599066217868763939419909216849255539123378331933017763101238907296429619957673479451002889682088451986894668538548370277499804057864344763404649938455326552512133957896454468215862173451643619511130828755367440458845645189914798544027674269732307846403005841327251397509337663412702901937794015707758185929527674836430482992606233067444837807460829303862409329398284320150205631739060228554840534843586112404269329795163378502751594933636283421108140184489075896958324102113283998063692980650702646000978106468755357199751531359344086777681847269282620105502946881642168187781666027487104220094403421285457763915092348330789675393758986904293364385285313757780584619260425156687466470410951429496109797255683067460339343631767542587227178489520664340700475044539139327350779183982664488107573844535846186720329521103907322461967989389990228837277864114375748458571526037921883895849670434416996586175469246637037727255826771628435101946859551754877137457709360326268675701425789008957519029160130015298165027025213372853729490475631827773513170597661748601750166508186470123002786831546051027391844267724026928815972545516493884454324905297015699149850324873739938025394413781542343584532420571640977235740657210215768621321135196042756225734707568752135694047660033652611574145140178349458163507466737029615898622062177464575852781522315963431272586007055517403280711236755874163459685159603908336490469412703509699402300334797857598312347685700448430107880768552376514661673907826774384410094620400380381822545219717880868432087289980815697451676637054173651143041777106763361008332595383282559682297501134380960817668408020500674812760097006444472778999002476602634329910206470935337753029058495718456491820409454397607387652362126706065731098991106761054278477888042822008591215993550061171642539464930158644329270313871982507242675204019863247323058908114602772135089064798381096423513471540694610561414281795333952666472887604826100063772868395916611277966816981964045719561000011414806203094756765910236327442411491877516715647719329197188806344225320800964629240809823932893116295590365005547297556010017141853493519327008319247058821827297190100534408019245602490212560595167878587375530044021303301514966857163711048430672804110796125447872013793758534153643026996609416212110917091217206265982125526630840621544455847939180083090635151921333454867691457480503869888071123233540272383300463476869271999148348605693537195317423380537026427073231791558183378314572647287492030594198989845758637297102144442073347059643750885521335544700642677116237530884175122859655362634093510453784503429605816342129692507158466937258481593048232672273273176862906774315591010855444342496177443020916638248805081693621385351241172747064945822424526859924948615028476517074637973462543570724982239057505948685448426046770449996850099131082876342453894153694607789553152139306254191180408240012930063113684477778606564671788220393956625450522004143545285648411622564988709136518122877591074985883154688355213932675813165770341310456809140296337292004569138749921630356070101742782409136365599109824358235226440496056480776809560490102157010589491771376432152487762936899075751204693698648045118497050228403003966233252419085880464203722916358528133354309985902114143944304650417271471191704273609283468726959876158033449166748778099932891196694411824745086478674689243923971732606993660969596873199050273148634342547582629488220535361936664483267225788697512468879162025582122251727051771875220246629080812447799720941927102144415484046681639633796148362360043444853688014495060688678216922190188773878287379550997793339954696700204509895053807358732669278818326225857027948511323653368024685394989469724515046124910462229157784625259630166688577711640103513954907170074999500797973494012301859729325857138825943359830417445677167164235899661503550017719989019398981750756654140525882466692084391556075562649946147274307816024317596292079444572823358377033777905006163868803723365654938580266375857408133957114318081516032613544414076399574507749505653631176679959206411376265267224910363734832217299031234543760163344081412945030068294038038534735714879887145120496681479101913284598283302379023181086139420345746579396800730205644031774543094468277504929568378042777469554137419373876443418097639743168565443594484510275711546806618210065947547158645404402087283471172846738444123711809522612430100829281018551996627433852127927395310704056289479642223216744960522115814869505078956213643321828360200621270073716741790192350437087516506462397653266627882263913477380258014863719444104413590938188224287747321987391816077847430002548880391390061011611119140596137751063010973737629841350470649597404671242010053820991304661992833432792194967631786937581924810637864734047899671665617289304797018773609866243334509145007249358713464031390307794962696243548100498345073465081397507124103526509690176715706479860993088490335936701239366173061735135998849228619868350104919384314582061646975346808959786549826374088579994487380912605900249322591911033754519695278781547752608863632996633746281879603058357327452724803276181415048005645931617091134567689057618058522792817391252153891945388265419223212627350603680664950375452015288606681565139978173089200107507366712195250759744146508224369683611073668131290946112621339743663578818886550099824331538339898224067211191849472520822545984110913092873024343752960360359889962016982356565075720498271882801402733192606180681431228484965522195714627898753077767431611261934070780345688929535295743586792473384615812929873802815202565243538616287742079493236126383926037437250114799849070787662749212768585719356160425400206759606384634934531103525864420775109439142795608600064603406546659565484874288317631530681161147311491558259998951863456892309236742643639634155158745824765558189275974949867841622157606118036325809511872849121460465691285380261405910932325228841062537722855607415637965032470371016433411395020365579016194169246794123221959025313527565794466675930723576143639161299922916118409945830233786813989230194836219936468177925639622283954886911780834316245285627584217918948361977380655456775536688433559503431972932467025829599914872751991889016816729807561406853222647922635915321649017068592493853129117572631558916794005405301282888619680008853528491291448853860614946438431000436845897095452736429393921385376859738907389114009779954780130115933124773956114549460824880850669162781653780128167087&action=last20&fr=0&to=100"]here is an example[/URL] !
We start with 7317 digit terms and divide the number of digits by two at each iteration.
I even think I could "make" some pretty funny aliquot sequences of similar types.
For example one that would start with a term of 8000 digits, and whose second term would have 7000 digits, and whose third term would have 6000 digits, ...[/QUOTE]I suspected, but hadn't played with such. Finding one in the wild was interesting. That's for the link.

EdH 2022-01-21 21:09

Base 71 is ready to be "tabled." Ir's all initialized with remaining cofactors >99 dd. It has one merge:[code]71^8:i2066 merges with 1578:i1856[/code]Moving to the high end of 968. . .

garambois 2022-01-22 08:42

OK Ed, a lot of thanks !

garambois 2022-01-22 18:16

I reserve the base 77 for initialization.

RichD 2022-01-22 18:53

Base 99 can be added at the next update. I'll start on base 97 next.

garambois 2022-01-22 19:46

Fantastic !
Thank you very much !

EdH 2022-01-22 20:15

Current Reservations of Tables Not Yet On Page
 
Since uninitialized tables aren't added to the page, there's no reservation reference (unless I'm just missing it). I'd like to use this post to try to keep track and provide a central point for reference. I'll try to edit this post whenever a table is added to the main pages or a new one reserved.

Base Reservations for Table Being Initialized:
[code]All covered by main page.
No further updates here.[/code] From time to time, I'll transfer this info to a newer post, so it will still be easily found.

As far as I can tell, the following bases <100 are uninitialized:[code]Ditto.[/code]

garambois 2022-01-23 09:22

Thank you very much Edwin for this initiative !
Updating and adding several bases takes me several hours and I can't do it very often anymore because of the large number of sequences there are now in the project and also because of my workload.
I remind you that the next update will take place on the weekend of February 5th and 6th.

As far as I'm concerned, you have to add the 88 base I'm currently working on, I'm initializing it.

To my knowledge, the bases <100 on which nobody is working are : 70, 76, 78, 80, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 98.

EdH 2022-01-23 14:10

[QUOTE=garambois;598617]. . .
As far as I'm concerned, you have to add the 88 base I'm currently working on, I'm initializing it.

To my knowledge, the bases <100 on which nobody is working are : [STRIKE]70[/STRIKE], 76, 78, 80, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 98.[/QUOTE]Base 70 is also ready to be "tabled." See post [URL="https://www.mersenneforum.org/showpost.php?p=598138&postcount=1402"]1402[/URL], which leads me to think that I'll rewrite my post to flag those bases that are finished as well, until they are added to the project pages. That should help a little.

Thanks Jean-Luc!

garambois 2022-01-23 14:28

Thank you very much Edwin.
Indeed, it is very clear like that !


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