  A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs
nanowire core is investigated in the low $E_J/E_C$ regime. Little-Parks
oscillations as a function of flux along the hybrid wire axis are destructive,
creating lobes of reentrant superconductivity separated by a metallic state at
a half-quantum of applied flux. In the first lobe, phase winding around the
shell can induce topological superconductivity in the core. Coherent qubit
operation is observed in both the zeroth and first lobes. Splitting of parity
bands by coherent single-electron coupling across the junction is not resolved
beyond line broadening, placing a bound on Majorana coupling, $E_M/h$ < 10 MHz,
much smaller than the Josephson coupling $E_J/h$ ~ 4.7 GHz.
