BACKGROUND: We found a strong selective 3-sites periodicity of deviations from randomness of the dinucleotide (DN) distribution, where both bases of DN were separated by 1, 2, K sites in prokaryotes and mtDNA. Three main aspects are studied. I) the specific 3 K-sites periodic structure of the 16 DN. II) to discard the possibility that the periodicity was produced by the highly nonrandom interactive association of contiguous bases, by studying the interaction of non-contiguous bases, the first one chosen each I sites and the second chosen J sites downstream. III) the difference between this selective periodicity of association (distance to randomness) of the four bases with the described fixed periodicities of base sequences. RESULTS: I) The 16 pairs presented a consistent periodicity in the strength of association of both bases of the pairs; the most deviated pairs are those where G and C are involved and the least deviated ones are those where A and T are involved. II) we found significant non-random interactions when the first nucleotide is chosen every I sites and the second J sites downstream until I = J = 76. III) we showed conclusive differences between these internucleotide association periodicities and sequence periodicities. CONCLUSIONS: This relational selective periodicity is different from sequence periodicities and indicates that any base strongly interacts with the bases of the residual genome; this interaction and periodicity is highly structured and systematic for every pair of bases. This interaction should be destroyed in few generations by recurrent mutation; it is only compatible with the Synthetic Theory of Evolution and agrees with the Wright's adaptive landscape conception and evolution by shifting balanced adaptive peaks.