Let $\mathbf{s} = (s_0, s_1, s_2, \ldots), s_i > 2$, be a sequence and let $\Delta_{\mathbf{s}}$ be the set of all sequences of nonnegative integers $\mathbf{a} = (a_0, a_1, a_2, \ldots)$ such that $a_i < s_i$. Let $\alpha_{\mathbf{s}}: \Delta_{\mathbf{s}} \to \Delta_{\mathbf{s}}$ be an addition by element $(1, 0, 0, \ldots)$ with carry over to the right, i.e. $\alpha_{\mathbf{s}}(x_0, x_1, x_2, \ldots) = (z_0, z_1, z_2, \ldots)$, where $z_0 = x_0 + t_0 \mod{s_0}, z_k = x_k + t_{k} \mod{s_k}$, where $t_0 = 1$ and $t_k = 0$ if $x_{k-1} + t_{k-1} < s_{k - 1}$ and $t_k = 1$ otherwise. The system $(\Delta_{\mathbf{s}}, \alpha_{\mathbf{s}})$ is called odometer.
I was told that odometers have some applications in generating algebraic structures, formal algorithms and some other programming stuff, but noone gave me some actual usage. I can hardly imagine what exactly are odometers used for.
It would be very helpful if anyone could give some actual usage of odometers, because they look very interesting to me, but I like to study concepts that I can imagine using in some way.
Hopefully this is not offtopic.
