[math-fun] Re: Number of ones in the binary expansion of 3^n (fwd)

6 Dec 2002

      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