The modular distribution of Stern’s sequence
The modular distribution of Stern’s sequence
Let $(s_n)_n$ be Stern’s sequence, $a, b, m \gt 0$ integers. The natural density of indices $n$ such that $(s_n,s_{n+1}) \equiv (a, b)\,{\rm mod}\, m$ exists and is determined. The main tools in the proof are the properties of the relevant automata.