10.5281/zenodo.19019498 This work presents a complete study of the Androsova series a_n = 3 + n(n+9)/2. It is proved that all 22 terms for n = 0..20 correspond to real isotopes. For each isotope, the proton number Z and neutron number N are determined. The valley of stability is constructed, and the limit N/Z ≈ 1.5 is found. The absence of proton magic numbers is shown. The connection with the numbers 137 and 256 is established. Based on the valley of stability, predictions are made for the next members of the series (n = 21..40 and n = 41..50). All calculations are presented in full to allow independent verification.