Version 2 - April 2026 This preprint presents a systematic analysis of numerical patterns in the periodic system, connecting Mendeleev's original insights with contemporary extensions to superheavy elements. The simple arithmetic mean between atomic numbers of homologous elements fails because p, d, f and predicted g subshells are inserted between periods. Adding half the electron capacity of the highest subshell crossed (K = 3 for p, 5 for d, 7 for f, 9 for g) restores the correct atomic number. Key updates from v1:- Systematic evaluation across 34 homologous triplets (Z ≤ 118)- Inclusion of p-subshell correction (K=3)- All tested cases reproduce with zero deviation (0.00 ± 0.00)- Updated figures showing systematic deviations- Expanded historical context and references The method follows the Madelung rule, offers no new physics, and serves as a structural tool for teaching and preliminary screening. Keywords: periodic table, atomic number, Mendeleev, superheavy elements, numerical patterns, Madelung rule
Rodrigo Leonard Barboza Rodrigues Filho (2026) studied this question.