Some properties of well-based sequences

S. V. Kitaev stated a problem of finding the number of well-based sequences and of existence of a bijection between these objects and sets associated with the sequence A103580. Well-based sequences define the class of graphs for which independent sets are enlisted by S. V. Kitaev. In our paper, the desirable bijection is obtained and it is proved that the number of well-based sequences increases as $\Theta(2^{n/2})$. Bibliogr. 5.