Abstract
We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. 174, 149–159 (1995)] by showing that the Rudin-Shapiro sequence is not palindromic, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schrödinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum.
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