We have searched for the simplest kaonic nuclear state, K̄NN, using the in-flight 3He (K-, n) reaction at the J-PARC hadron experimental facility. In the semi-inclusive neutron missing-mass spectrum at θnlab=0°, an excess of yield was observed just below the K- pp mass-threshold, which cannot be explained by any elementary reactions [PTEP 2015, 061D01]. To understand the missing-mass spectrum of 3He (K-, n) X, we investigated the elementary (K-, n) reactions using hydrogen and deuterium targets. The p (K-, n) X missing-mass spectrum was well described by the charge-exchange reaction. However, in the d (K-, n) X spectrum, we observed an excess of yield just below the K- p mass-threshold, which was similar to that in the 3He (K-, n) X spectrum.