Recognition-encoded melamine oligomers (REMO) are synthetic polymers that feature an alternating 1,3,5-triazine-piperazine backbone and side-chains equipped with either a phenol or phosphine oxide recognition unit. An automated method for the solid-phase synthesis (SPS) of REMO of any specified sequence has been developed starting from dichlorotriazine monomer building blocks. Complementary homo-oligomers with either six phenols or six phosphine oxides were synthesized and shown to form a stable duplex in nonpolar solvents by NMR denaturation experiments. The duplex was covalently trapped by equipping the ends of the oligomers with an azide and an alkyne group and using a copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction. The SPS methodology was adapted to synthesize mixed sequence libraries by using a mixture of two different dichlorotriazine building blocks in each coupling cycle of an oligomer synthesis. The resulting libraries contain statistical mixtures of all possible sequences. The self-assembly properties of these libraries were screened by using the CuAAC reaction to trap any duplexes present. In mixed sequence libraries of 6-mers, the trapping experiments showed that only sequence-complementary oligomers formed duplexes at micromolar concentrations in dichloromethane. The automated synthesis approach developed here provides access to large libraries of mixed sequence synthetic polymers, and the covalent trapping experiment provides a convenient tool for screening functional properties of mixtures. The results suggest high-fidelity sequence-selective duplex formation in mixtures of 6-mer sequences of the REMO architecture.