R: Re: Goodstein expansion

*To*: mathgroup at smc.vnet.net*Subject*: [mg132329] R: Re: Goodstein expansion*From*: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>*Date*: Tue, 11 Feb 2014 02:56:42 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20140209094907.18FA669F4@smc.vnet.net>

Many thanks to Bob Hanlon, Bill Rowe and Murray Eisenberg who pay attention to my question. I have to add some points. 1) the expansion I called Goodstein must be called more correctly Cantor expansion. 2) Cantor expansion is the usual base b power expansion where also exponents (if the case when >b) must be similarly expanded as in the example 87 = 2^6+2^4+2^2+1 = 2^(2^2+2)+2^(2^2)+2^2+2^0 where 6 and 4 are expanded too ("graphically" you must see only b's or numbers less than b). The Goodstein sequence is essentially obtained increasing base b to b+1 : GoodsteinProcess : Given a number m1 , write m1 in base-2-CantorForm. Replace 2 with 3 and obtain a new number n1. Expand m2=n1-1 in base-3-CantorForm Replace 3 with 4 and obtain a new number n2 Expand m3=n2-1 in base-4-CantorForm etc.. Property: this process terminates at 0 for any starting m1. I am asking an help in building a CantorForm[m,b] procedure in a simple way, when exponents becomes large and they also have to be expanded. Regards, Roberto RSE SpA ha adottato il Modello Organizzativo ai sensi del D.Lgs.231/2001, in= forza del quale l'assunzione di obbligazioni da parte della Societ=E0 avvie= ne con firma di un procuratore, munito di idonei poteri. RSE adopts a Compliance Programme under the Italian Law (D.Lgs.231/2001). Ac= cording to this RSE Compliance Programme, any commitment of RSE is taken by= the signature of one Representative granted by a proper Power of Attorney.= Le informazioni contenute in questo messaggio di posta elettronica sono ris= ervate e confidenziali e ne e' vietata la diffusione in qualsiasi modo o for= ma. Qualora Lei non fosse la persona destinataria del presente messaggio, La= invitiamo a non diffonderlo e ad eliminarlo, dandone gentilmente comunicazi= one al mittente. The information included in this e-mail and any attachments= are confidential and may also be privileged. If you are not the correct rec= ipient, you are kindly requested to notify the sender immediately, to cancel= it and not to disclose the contents to any other person.

**References**:**Re: Goodstein expansion***From:*Bill Rowe <readnews@sbcglobal.net>