Math-fun, I forwarded Allan's email to Philippe Dumas. H. ---------- Forwarded message ---------- Date: Fri, 6 Dec 2002 12:52:44 +0100 From: Philippe Dumas <Philippe.Dumas@inria.fr> To: Helger Lipmaa <helger@tcs.hut.fi> Subject: [math-fun] Re: Number of ones in the binary expansion of 3^n (fwd) Helger Lipmaa writes: do you know an answer to this problem? H. I know only this is a very difficult one. Cobham's theorem says that a 3-rational sequence cannot be a 2-rational sequence, unless it is rational in the classical sense. (This is folklore, and there is a proof only for automatic sequences, that is rational sequences which take only a finite number of values). Here the sequence is evidently 3-rational and certainly not rational in the classical sense. For more, ask Jean-Paul Allouche (http://www.lri.fr/~allouche/, allouche@lri.fr). Give him my name. Best regards, Philippe