In this work, we study the lepton flavor and lepton number violating $B_{c}$ meson decays via two intermediate on-shell Majorana neutrinos $N_j$ into two charged leptons and a charged pion $B_{c}^{pm} to mu^{pm} N_j to mu^{pm} tau^{pm} pi^{mp}$. We evaluated the possibility to measure the modulation of the decay width along the detector length produced as a consequence of the lepton flavor violating process, in a scenario where the heavy neutrinos masses range between $2.0$ GeV $leq M_N leq 6.0$ GeV. We study some realistic conditions which could lead to the observation of this phenomenon at futures $B$ factories such HL-LHCb.
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