We study theoretically the kaonic atom and kaonic nucleus formations in the in-flight (K − , p) reactions using the Green function method, which is suited to evaluate formation rates both of stable and unstable bound systems. We consider 12 C and 16 O as the targets and calculate the spectra of the (K − , p) reactions. We conclude that no peak structure resulting from kaonic nucleus formation is expected in the reaction spectra calculated with the chiral unitary kaon-nucleus optical potential. In the spectra with the phenomenological deep kaon-nucleus potential, it may be possible to observe some structures because of the formation of the kaonic nucleus states. For all cases, we find clear signals because of the kaonic atom formations in the reaction spectra, which show very interesting structures, such as the RESONANCE DIP instead of the resonance peak for the atomic 1s state formation.