[seqfan] Re: Is this sequence interesting: Möbius mu values as a (possibly irrational) balanced ternary number

[Robert Gerbicz]

2012/8/9 Charles Greathouse <charles.greathouse at case.edu>

> Surely irrational, else they would repeat?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Thu, Aug 9, 2012 at 3:35 PM, Alonso Del Arte
> <alonso.delarte at gmail.com> wrote:
> > \sum_{n = 1}^\infty \mu(n) 3^{-n}
> >
> > = 3^(–1) – 3^(–2) – 3^(–3) – 3^(–5) + 3^(–6) – 3^(–7) + 3^(–10) – ...
> >
> > = 0.1819953867026338878...
> >
> > Al
> >
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And it is not normal in base 3 as it does not contain the string 1111 (in
base 3)=40 (in base 10). Just use that among 4 consecutive numbers you will
see moebius=0, because one of them is divisible by 4.