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We call a positive real number $\lambda$ admissible if it belongs to theLagrange spectrum and there exists an irrational number $\alpha$ such that$\mu(\alpha)=\lambda$. Here $\mu(\alpha)$ denotes the Lagrange constant of$\alpha$ - maximal real number $c$ such that $\forall \varepsilon>0$ theinequality $|\alpha-\frac{p}{q}|\le\frac{1}{(c-\varepsilon)q^2}$ has infinitelymany solutions for relatively prime $p$ and $q$. In this paper we establish anecessary and sufficient condition of admissibility of the Lagrange spectrumelement and construct an infinite series of not admissible numbers.

Admissible endpoints of gaps in the Lagrange spectrum