The Al27(p,n)Si27, Si29(p,n)P29, and P31(p,n)S31 ground-state reactions have been measured using polyethylene "long counters." Absolute cross sections and angular distributions were obtained from 0° to 160° at 10° intervals. The measured angular distributions were compared with the predictions of an optical-model calculation, using an optical potential suggested by Lane, which is a function of the isotopic spins of the incident proton and target nucleus. Since the ground-state (p,n) reactions were measured below the threshold for the excited state, the proton incident energies were between 5.8 and 7.6 MeV. Because of this low proton energy, the optical-model calculations include both Coulomb effects of distortion of the proton wave and the Coulomb energy difference between the incoming proton and the outgoing neutron. Fair agreement between the theoretical and experimental results was obtained for Si29 and P31 using a surface interaction for the imaginary and isobaric parts of the optical potential. Furthermore, the angular distributions from these two nuclei were quite similar in structure, in agreement with the twin-reaction hypothesis of Bloom, Glendenning, and Moszkowski. The neutron angular distributions from Al27 are quite different in structure from those obtained from Si29 and P31, and attempts to fit them with the optical-model calculation were not successful. A calculation based on distorted-wave single-particle excitation with charge-exchange was also carried out. The results of this calculation agree with those of the optical model for Si29 and P31. For the Al27 reaction the results of the DWBA calculation are different from those of the optical model, since in the former calculation momentum transfers greater than zero are included; however, neither calculation fitted the Al27 data.