Another Aliquot Sequence site

[schickel]

I was perusing Paul zimmerman's aliquot page and noticed a new link to a site by Jean-Luc Garambois. Unfortunately, it is in French. The machine translators available (Babelfsh and Google) don't do a very good job of translating the pages to a readable form; is there anyone that could consider making an English translation available?

[firejuggler]

I know I said i would translate anything in french to english, but if there is too much math, I might not do a better job than google. What part do you want translated?
pair = even
impair= odd
nombre premiers= prime number

[fivemack]

Yes, I'm fluent in French, but there's quite a lot of material there and translating it all at once would be a big job.

He has proved that, for any X and N there exist aliquot sequences which go up by at least a factor X at each iteration, for at least N iterations.

In http://www.aliquotes.com/problemes.htm there is a list of sequences which he'd like to have pursued to the first iteration at which the number less-than-doubles (ie often until they lose 2^3*3*5); some of the ones >1000000 have only been taken to 93 digits and so would be easy to take for another thirty digits (~100 iterations), though 19560 still has the doubling at 169 digits.

[Andi47]

Originally Posted by fivemack

In http://www.aliquotes.com/problemes.htm there is a list of sequences which he'd like to have pursued to the first iteration at which the number less-than-doubles (ie often until they lose 2^3*3*5); some of the ones >1000000 have only been taken to 93 digits and so would be easy to take for another thirty digits (~100 iterations), though 19560 still has the doubling at 169 digits.

This sounds like a possible subproject for our aliquot project.

(and no, I can't translate this site - my French is q quite rusty, so my translation might be as bad as a google translation.)

[schickel]

Originally Posted by fivemack

Yes, I'm fluent in French, but there's quite a lot of material there and translating it all at once would be a big job.

Even just a quick summary would be more helpful than the auto-translation. When they do it, it destroys the formatting, breaking the flow of the page.

He has proved that, for any X and N there exist aliquot sequences which go up by at least a factor X at each iteration, for at least N iterations.

In http://www.aliquotes.com/problemes.htm there is a list of sequences which he'd like to have pursued to the first iteration at which the number less-than-doubles (ie often until they lose 2^3*3*5); some of the ones >1000000 have only been taken to 93 digits and so would be easy to take for another thirty digits (~100 iterations), though 19560 still has the doubling at 169 digits.

I think we filled in the work under 1M when we computed all the sequences up to 100 digits....

Originally Posted by Andi47

This sounds like a possible subproject for our aliquot project.

Should we have a poll about that, or should we just dive right in?

(and no, I can't translate this site - my French is q quite rusty, so my translation might be as bad as a google translation.)

I haven't investigated the auto-translators much. If you contribute to improving the translation of a page, does it flow through to people that come after you?

Maybe just check the translation and help smooth out problems (I assume the machines have trouble with jargon and colloquialisms.)

I'll take a look after work today and see if I can get a better sense of where the major problems are...

[schickel]

Originally Posted by firejuggler

I know I said i would translate anything in french to english, but if there is too much math, I might not do a better job than google. What part do you want translated?
pair = even
impair= odd
nombre premiers= prime number

Actually not much math....as noted, trying to read the machine translations breaks the page formatting and makes it hard to follow the flow.

Maybe we could make this a community effort (we could work on a full translation when we get tired of watching paint dry....)

[EdH]

Originally Posted by schickel

Actually not much math....as noted, trying to read the machine translations breaks the page formatting and makes it hard to follow the flow.

Maybe we could make this a community effort (we could work on a full translation when we get tired of watching paint dry....)

I could point a couple of my steam-driven machines in a new aliquot direction, but mon français is worse than mein Deutsch...

[firejuggler]

ok then allow me

Bienvenue à tous sur ce site consacré aux suites aliquotes.          Il existe déjà plusieurs autres sites qui traitent de ce sujet. Il y a même redondance.
        Ce site présente surtout nos travaux inédits dont nous n’avons pas retrouvé le contenu ailleurs.

            Vous êtes sur un site actif de recherche sur les suites aliquotes.

            On y présente des conjectures dont certaines pourront devenir des  théorèmes démontrés alors que d'autres pourront être abandonnées au fur  et à mesure que les recherches avancent.

                Ainsi, depuis que ce site a été mis en ligne le 8 septembre 2010,  il a permis une avancée majeure dans la connaissance des suites  aliquotes : ce qui était ici présenté comme la deuxième conjecture de  Garambois est devenu le théorème de Barbulescu Garambois.

            En fait, la raison d’être de ce site est surtout la dernière partie :  « Les problèmes ouverts ». En effet, nous avons besoin d'aide pour  faire avancer encore les recherches, car certaines questions nous  semblent ardues et d'autres demandent de la patience pour faire des  programmes et surtout pour les faire tourner et attendre les résultats !

        Dans un premier temps, nous allons cependant faire une entorse à notre  règle : nous allons rappeler les définitions relatives aux suites  aliquotes.          Puis, nous rappellerons quels sont les différents comportements des  suites aliquotes, en y ajoutant à chaque fois les choses nouvelles          que nous avons remarquées à leur sujet et que nous n’avons trouvées  sur nul autre site, ni dans les livres.
        Ensuite, nous présenterons des tentatives de généralisation des suites  aliquotes où nous avons essayé d’autres processus itératifs, mais aussi  de traiter le problème en étendant la fonction σ’ à d’autres objets  mathématiques que les entiers comme par exemple les nombres complexes  entiers de Gauss ou les polynômes.
        Enfin, la dernière partie, « Les problèmes ouverts », expose  directement les questions encore non résolues par nous et probablement  par personne d'autre qui restent ouvertes.          Cette partie peut être lue indépendamment de tout le reste qui peut  cependant donner des idées pour la résolution des problèmes ouverts.          Grâce à cette partie, tout visiteur peut lui-même devenir acteur et  prendre part aux recherches sur les suites aliquotes.Toute personne  arrivant à résoudre un de ces problèmes ouverts aura alors contribué à  faire avancer la recherche sur les suites aliquotes et aura gagné le  droit d’être cité !
        Notons pour finir que notre but est juste de découvrir certains des  nombreux secrets que cachent les suites aliquotes et peut-être même l'ultime  Secret des suites aliquotes, s'il existe... quoique pour le moment,  nous n'ayons encore pas la moindre idée de ce à quoi il pourrait  ressembler !         
Pour toutes ces parties, des liens permettent de voir les démonstrations  ainsi que les méthodes qui ont permis d’arriver aux affirmations et aux  conclusions avancées.


         Définition : les fonctions σ et σ', suites aliquotes et antécédents aliquotes

          Les suites aboutissant à 1

          Les suites aboutissant sur une chaîne aliquote, les chaînes aliquotes isolées

          Les  suites aliquotes à statut inconnu, conjecture de Catalan, conjecture de  Garambois N°1 argumentée allant à l’encontre de la conjecture de  Catalan et théorème de Barbulescu Garambois (théorème sur la vitesse de  croissance de séquences de suites aliquotes)

      Les suites aliquotes à très forts coefficients de croissance

          Les suites aliquotes exotiques

          Problèmes ouverts théoriques et défis pour les programmeurs

 

        
         Site crée par :

         GARAMBOIS Jean-Luc
        BARRET Cédric
        HUBER Olivier
        BACHSCHMIDT Matthieu

                  Remerciements :

         A Jean-Paul DELAHAYE qui a fait mention de nos travaux dans la revue  Pour le Science, dans le numéro de février 2002. Cette publication nous a  rendus crédibles et nous a très fortement motivés !
        A Paul ZIMMERMANN qui a entrepris de gros calculs pour résoudre les  défis que nous proposons aux programmeurs et qui a permis à notre équipe  de décupler sa puissance de calcul !
        A Razvan BARBULESCU qui en la démontrant, a transformé une de nos  conjectures en théorème et qui a de plus résolu un de nos problèmes  théoriques posés !
        A Francis JAMM pour son aide pour certaines démonstrations, pour ses relectures.
 Egalement à Pierre TOUGNE, Mathieu MOUGEY, Jean-Luc GRAFF, David KOLODZIEJ et Alain STAMM.

         
        Prise de contact :

        jlgarambois at gmail.com
        Mettre en objet en lettres capitales : SUITES ALIQUOTES

                    Dernière modification : Mai 2011

Welcome to this site about aliquot sequences. there is other site on this particular subject. There is even some redondancy. This site is mostly about our exclusive (personal, unique) work, wich we didn't find about elsewhere.

You are on a active site of aliquot sequence research.

We present here some conjecture that could be proven, some other will be abandonned once further advance in research is done.

So, since the online relase of this site on the 8 th september 2010, it allowed a major breakthrough in the aliquot sequence knowledge : What was presented here as Garambois's second conjecture as become the Barbulescu-Garambois's theorem.

In fact, the reason of existence of this site is mostly for the last part : the open problems. Indeedn we need help to further our research, as some question seem hard(to answer) and other as they require patience to make software and make them return results.

First, we will present the definition used in aliquot seqs. Then, we will remind of the different evolution of aliquot sequence, adding new data about them wich have not been found in any other book/site ( we read/reviewed).

Second, we will present tentative generalisation about aliquot sequence where we tried alternative iterative process, but also the problem of the extention of the function σ’ to other mathematical object, like Gauss's complex integer Or polynomial.

In last part, "the open problems" expose directly the non resolved question by anybody ( open problems : read unfinished sequence) and still unanswered. This part can be read independantly of the rest and can give idea for the "open problem" resolution. Thank to that , any visitor can become a part of the search on the AS. Anybody that manage to finish one of those "open problem" will have contributed to the research on AS , and will be granted a citation!
Please note that our goal is to discover some of the numerous secret that AS hide, and maybe the Ultimate Secret of the AS, if it exist... Though, for the momment, we do not have the slightest idea of what it is.
For all those part, links will let you read demonstration and method which allow us to get to those affirmation and conclusion

<link>
-Definition : function σ and σ’, AS, and preceding AS ( from one iteration , get to the one before)
-AS ending in 1
-Merging AS and isolated AS
-AS with unknow status, Catalan conjecture, first argumented Garambois 's conjecture against Catalan's and Barbulescu-Garambois 's conjecture ( theorem obaout the speed of growing AS)
-AS with wery high growing speed
-exotic AS
-theoric Open problem abd challenge for software writer
</link>


Site created by
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Thanks
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contact
jlgarambois at gmail.com
put in object (in maj): SUITES ALIQUOTES
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I hope I did a satisfacting job on the translation. Other might object.
note : in Italic, My explanation, escuse and hesitation.

[firejuggler]

This guy seem to not know about yafu/msieve and aliqueit and ggnfs. Should we ask?

[fivemack]

Originally Posted by schickel

I think we filled in the work under 1M when we computed all the sequences up to 100 digits

You filled in some of it, but to answer his question requires to carry each of the sequences until they lose the 2^3*3*5 driver (and possibly longer in case they lose it in favour of a worse driver), which is often a bit further than we have taken them, and may be an awfully long way.

In http://www.aliquotes.com/problemes.htm, 'Résolution' means someone's working on it, and 'RESOLU' means it has been taken to a point where it lost the driver.

[fivemack]

Originally Posted by schickel

Actually not much math....as noted, trying to read the machine translations breaks the page formatting and makes it hard to follow the flow.

The page formatting looks OK to me looking through google-translate into English.