EN|RU Volume 18, No 1, 2011, P. 15-19 UDC 519.2 A. A. Valyuzhenich Some properties of well-based sequences Abstract: 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. Keywords: well-based sequence, sum-free set. Valyuzhenich Alexander Andreevich 1 1. Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia e-mail: graphkiper@mail.ru © Sobolev Institute of Mathematics, 2015