Four new transition metal-free pnictide representatives of the LaOAgS structure type were predicted by DFT calculations and found in the BaFMgPn (Pn = P, As, Sb and Bi) family. The compounds adopt the tetragonal space group P4/nmm with the unit cell parameters a/c 4.3097(1) angstrom/9.5032(1) angstrom, 4.3855(1) angstrom/9.5918(1) angstrom, 4.5733(1) angstrom/9.8184(1) angstrom, and 4.6359(1) angstrom/9.8599(1) angstrom, respectively. According to the DFT calculations, these new compounds are semiconductors with band gaps steadily decreasing from Pn = P (ca. 2 eV) to Pn = Bi (ca. 1 eV). The corresponding strontium fluoride and rare-earth oxide analogs are unlikely to exist and have not been observed yet. The trends of the stability within 1111 and structurally and/or chemically related compounds based on a combined consideration of geometry and DFT calculations are discussed.