Transcendence of Numbers with a Low Complexity Expansion Original Research Article

A sequence is Sturmian if it has complexityn+l−1, that is,n+l−1 factors of lengthnfor everyn; we show that real numbers whose expansion in some basekgreater-or-equal, slantedlis Sturmian are transcendental, and give explicit expressions for these numbers. We then generalize the transcendence property to other sequences of low complexity, particularly the Arnoux–Rauzy sequences.