Investigations of the existence of pentaquark states containing a single $b$ (anti)quark decaying weakly into four specific final states J/$psi K^+pi^- p$, J/$psi K^- pi^- p$, J/$psi K^- pi^+ p$, and $J/psi phi (1020) p$ are reported. The data sample corresponds to an integrated luminosity of 3.0/fb in 7 and 8 TeV pp collisions acquired with the LHCb detector. Signals are not observed and upper limits are set on the product of the production cross section times branching fraction with respect to that of the $Lambda_b$.