On the condensation points of the lagrange spectrum
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For a positive integerN, L(N) denotes the set of Lagrange values of all sequences (a k:k=0, ±1, ±2,…) of positive integers with lim sup k ak=N. It is shown that for anyN≥3L(N) has infinitely many condensation points. Such points can be realized as Markov values of symmetric doubly periodic sequences whose period consists of a semi-symmetric tuple.
KeywordsPositive Integer Distinct Element Continue Fraction Accumulation Point Infinite Sequence
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