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\def\RR{{\mathbb R}}

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Consider the sequence of positive integers $(u_n)_{n\geq 1}$
defined by $u_1=1$ and
$u_{n+1}=\lfloor\sqrt{2}\left(u_n+\frac{1}{2}\right) \rfloor$.
Graham and Pollak discovered the unexpected fact that
$u_{2n+1}-2u_{2n-1}$ is just the $n$-th digit in the binary
expansion of $\sqrt{2}$. Fix $w\in \RR_{>0}$. In this note, we
first give two infinite families of similar nonlinear recurrences
such that $u_{2n+1}-2u_{2n-1}$ indicates the $n$-th binary digit
of $w$. Moreover, for all integral $g\geq 2$, we establish a
recurrence such that $u_{2n+1}-gu_{2n-1}$ denotes the $n$-th digit
of $w$ in the $g$-ary digital expansion.

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