The thermodynamic preference of a foreign atom for adsorption on versus intercalation into a graphitic surface is of fundamental and widespread interest. From an exhaustive first-principles density functional theory investigation for 38 typical elements over the periodic table, we reveal a quasilinear correlation between the Shannon effective ionic radius and the chemical-potential difference for a single atom from adsorption to intercalation at multilayer graphene surfaces. A critical Shannon radius is found to be around 0.10 nm, below (above) which intercalation (adsorption) is more favorable for elements with ionic-like bonding after intercalation. Single atoms with van der Waals-biased bonding show some deviation from the linear relationship, while single atoms for the elements with covalent-like bonding do not favor intercalation relative to adsorption. An energy decomposition analysis indicates that the chemical-potential difference determining the thermodynamic preference of a foreign atom for adsorption versus intercalation results from the competition between the electronic and elastic strain effects.