Three new short-lived positron emitters, P28, Cl32, and Sc,40 of the nuclear series Z=2n+1, A=4n have been produced by p-n reactions using 20-Mev protons from the UCLA 41-in. FM cyclotron. Al24 has also been investigated. Al24 has a half-life of 2.10+/-0.04 sec and five gamma rays from 1.39 Mev to 7.12 Mev. 2-Mev alpha particles are emitted in a small fraction of the decays. P28 has a half-life of 0.280+/-0.010 sec, threshold of 15.6+/-0.5 Mev, eight gamma rays from 1.79 Mev to 7.59 Mev, and positrons of maximum energy 10.6+/-0.4 Mev. No heavy particles were detected in the decay. Cl32 has a half-life of 0.306+/-0.004 sec, threshold of 14.3+/-0.5 Mev, four gamma rays from 2.21 Mev to 4.77 Mev, and positrons of maximum energy 9.5+/-0.4 Mev. 2-3 Mev alpha particles are emitted in a small fraction of the decays. Sc40 has a half-life of 0.22+/-0.03 sec, threshold of 15.9+/-1.0 Mev, a 3.75+/-0.04 Mev gamma ray, and maximum positron energy of 9.0+/-0.4 Mev. No heavy particles were detected in the decay. Possible decay schemes can be set up which involve favored positron transitions to calculated analog levels in the daughters in the cases of Al24, P28, and Cl32. In the P28 decay, the positron component to the 1.78-Mev level in Si28 has the same ft value as the negatron decay to this level from Al28, thus indicating the similarity of the nuclear wave functions of P28 and Al28.