  Starting with the pioneering work of Ein and Lazarsfeld restrictions on
values of Seshadri constants on algebraic surfaces have been studied by many
authors. In the present note we show how approximation involving continued
fractions combined with recent results of Kuronya and Lozovanu on Okounkov
bodies of line bundles on surfaces lead to effective statements considerably
restricting possible values of Seshadri constants. These results in turn
provide strong aditional evidence to a conjecture governing the Seshadri
constants on algebraic surfaces with Picard number 1.
