A systematic study of the low-lying structure of N = 27, 28, and 29 isotones is performed within the shell model framework using the SDPF-U interaction [F. Nowacki and A. Poves, Phys. Rev. C 79, 014310 (2009)]. For each isotonic chain, correlation energy is found to increase while moving away from the stability line. Spherical shapes as well as small values of correlation energy are associated with the isotopes of 20 Ca and 19 K discussed in this study. Neutron intruder states appear at low excitation energy in the 18 Ar and 17 Cl studied isotopes. Coexistence between spherical and prolate deformed states is a systematic feature in 16 S isotopes. Below Z = 16 most of the studied nuclei are characterized by intruder ground states. The major role played by protons in determining the structure of N 28 nuclei is shown.