Suites de longueur minimale associees a un ensemble normal donne

For a given subsetA of the set of real numbers, we search a sequence Λ=(λ _n) of real numbers such that bothA is the normal setB(Λ) associated to Λ, and Λ takes its values in a bounded interval, with a minimal lengthM. A lower bound ofM is obtained, which gives some necessary conditions of existency of such a bounded sequence Λ. More details are given whenA is a subset of the set of integers. In this case, the problem is to find a polynomialQ of lowest degree such that the productP.Q has non-negative coefficients, for some special given polynomialP.