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Thanks to an observation by R. Robinson, for any
positive real $\alpha$ the function $\lambda n.\lfloor
n\alpha\rfloor$ mapping positive integers $n$ to the integer part
$\lfloor n\alpha \rfloor$ of $n\alpha$ (called the Beatty sequence
corresponding to $\alpha$) is computable if and only if $\alpha$
is (Cauchy) computable. For any $\alpha\in\mathbb{R}^{\geq 0}$,
oracle $A$, and $r\geq 1$, we show that $\lambda n.\lfloor
n\alpha\rfloor$ has a $\Delta_{r}^{A}$ graph if and only if
$\alpha$ is of class $\Delta_{r}^{A}(\mathbb{R})$ in the recently
introduced Zheng-Weihrauch (Z-W) hierarchy. If
$\alpha\in\Sigma_{r}^{A}(\mathbb{R})\cup \Pi_{r}^{A}(\mathbb{R})$,
then the above function is of class $\Delta_{r+1}^{A}$. We
consider $\lambda n.\lfloor n\alpha +\gamma\rfloor$ and show that
the {\it if} part corresponding to the next to the last statement
still holds (when now both coefficients are in
$\Delta_{r}^{A}(\mathbb{R})$). We prove the converse when $\alpha$
is irrational. If $\alpha$ is rational, then the function is
always primitive recursive (even for $\gamma$'s beyond the Z-W
hierarchy). Finally, we show that the set of (indices of)
computable Beatty sequences is $\Pi_{2}$.
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