The electronic properties of carbon nanotubes with the controlled chirality indexes have been studied. Via the DFT LSDA method using the Gaussian 03W and TubeGen software it has been found that semiconducting SWCNTs of small diameters (about 0.3 - 2 nm) have nonmonotonic oscillating character of their band gap dependence on the diameter. The nonmonotonic oscillating change of the band gap width, related to small magnitudes of the chirality indexes defining the SWCNTs symmetry and curvature, has been revealed. For very small diameters of chiralities (0, 4), (0, 5) the degeneration of the band structure leading to metallic properties and violation of the so-called '3K' rule has been found.