In this Letter, we experimentally demonstrate structured light carrying multiple values of orbital angular momentum (OAM) in the farfield scattering region of Vogel spiral arrays of metallic nanoparticles. Using Fourier-Hankel mode decomposition analysis and interferometric reconstruction of the complex amplitude of scattered waves, we show the ability to encode well-defined numerical sequences, determined by the aperiodic spiral geometry, into azimuthal OAM values, in excellent agreement with analytical scattering theory. The generation of azimuthal sequences of OAM values by light scattering from engineered aperiodic surfaces is relevant to a number of device applications for secure optical communication, classical cryptography, and quantum cryptography.