Three dimensional topological insulators (TIs) are novel materials with a conducting surface covering an insulating bulk interior. We examine the topological properties of nanowires of TI Bi_0.83Sb_0.17 and observed that they display oscillations of the magnetoresistance (MR) that can be interpreted as topological surface electronic transport. In this work, we study the nanowires at various magnetic field orientations, at low temperatures (1.5 K ≤ T < 5 K), and for field strengths up to 14 T. In the 4 T < B < 10 T range we observe B-periodic, Aharonov–Bohm (AB) oscillations of longitudinal MR with two periods, namely, one flux quantum Φ₀ and half of flux quantum Φ₀/2 (ΔB₁ = Φ₀/S, ΔB₂ = Φ₀/2S, where S is the cross-sectional area of the nanowire). The periods depend on the angle α between the magnetic field and the wire axis according to a cosine law that indicates that the phenomenon is governed by the axial flux enclosed by the nanowire. In additional to the high magnetic field oscillations, in the low magnetic field range, B < 4 T, we observe a conductance maximum for zero magnetic field and the first magnetoresistance maximum for Φ = Φ₀/2.