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The Ruler function has the following property:

$\forall n \in \mathbb{N}: f(2n) = f(n)+1,\, f(2n+1) = 1.$

Is there any other function with this property?

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    I somehow missed your question to me; anyway, what that line in the OEIS listing means is that, letting $f(n)$ be the ruler function, $\frac{\zeta(s)}{1-2^{-s}}=\sum_{k=1}^\infty \frac{f(k)}{k^s}$. That is, $\frac{\zeta(s)}{1-2^{-s}}$ is the *Dirichlet generating function* for $f(k)$.2011-09-02

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