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Let $b$ be an algebraic number with $|b|>1$ and $\mathcal{H}$ a finite set ofalgebraic numbers. We study the transcendence of numbers of the form$\sum_{n=0}^\infty \frac{a_n}{b^n}$ where $a_n \in \mathcal{H}$ for all$n\in\mathbb{N}$. We assume that the sequence $(a_n)_{n=0}^\infty$ is generatedby coding the orbit of a point under an irrational rotation of the unit circle.In particular, this assumption holds whenever the sequence is Sturmian. Ourmain result shows that all numbers of the above form are transcendental. Wemoreover give sufficient conditions for a finite set of such numbers to belinearly independent over~$\bar{\mathbb{Q}}$.

On the transcendence of a series related to Sturmian words