We look for predictive flavour patterns of the effective Majorana neutrino mass matrix that are compatible with current neutrino oscillation data. Our search is based on the assumption that the neutrino mass matrix contains equal elements and a minimal number of parameters, in the flavour basis where the charged lepton mass matrix is diagonal and real. Three unique patterns that can successfully explain neutrino observables at the $3sigma$ confidence level with just three physical parameters are presented. Neutrino textures described by four and five parameters are also studied. The predictions for the lightest neutrino mass, the effective mass parameter in neutrinoless double beta decays and the CP-violating phases in the leptonic mixing are given.
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