The competition between chain stiffness and chain collapse gives rise to complex low temperature morphologies of single polymer chains, in our case alkanes. These structures are characterized by specific sequences of dihedral angles along the chain, i.e., dihedral angle correlations extending beyond local steric effects. To describe and classify these morphologies, one can transfer concepts from protein science, where this creation of dihedral angle correlations underlies the formation of α-helices and β-sheets. We show here by means of flat-histogram Monte Carlo simulations that, although lacking in primary structure being simple homopolymers, short alkane chains fold into non-trivial ground states (tertiary structure) consisting of chain segments of defined secondary structures. The folded lamellar crystal typical for polyethylene chains requires a minimum chain length to occur as the ground state folded structure, which we identify to be around 150 repeat units.