In this letter, a novel pattern synthesis algorithm that jointly optimizes the number, positions, and excitation of elements in a sparse linear array (SLA) is designed based on continuous compressed sensing. The pattern synthesis problem is first formulated as a sparse recovery problem, which can be solved using semidefinite programming involving atomic norm minimization (ANM). The parameters of the designed SLA, including the corresponding element positions and excitations, are determined via Vandermonde decomposition and least squares in the continuous domain. As ANM works directly in the continuous domain, the proposed algorithm is able to synthesize the desired patterns with a small mismatch and a small number of elements. A number of representative numerical experiments show the effectiveness of our algorithm.