We study the periods of Markov sequences, which are derived from the continued fraction expression of elements in the Markov spectrum. This spectrum is the set of minimal values of indefinite binary quadratic forms that are specially normalised. We show that the periods of these sequences are palindromic after a number of circular shifts, the number of shifts being given by Stern’s diatomic sequence.
Markov sequence Stern’s diatomic series Stern’s diatomic sequence palindromic sequence evenly palindromic Christoffel words
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I. Urbiha, “Some properties of a function studied by De Rham, Carlitz and Dijkstra and its relation to the (Eisenstein) Stern’s diatomic sequence,” Math. Commun. 6, 181–198 (2001).MathSciNetzbMATHGoogle Scholar