A linear complexity analysis of quadratic residues and primitive roots spacings

We investigate the linear complexities of the periodic 0-1 infinite sequences in which the periods are the sequence of the parities of the spacings between quadratic residues modulo a prime p, and the sequence of the parities of the spacings between primitive roots modulo p, respectively. In either case, the Berlekamp-Massey algorithm running on MAPLE computer algebra software shows very good to perfect linear complexities.