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The ALICE Collaboration has measured the energy dependence of exclusive photoproduction of J/ψ vector mesons off proton targets in ultra–peripheral p–Pb collisions at a centre-of-mass energy per nucleon pair sNN−−−√=5.02 TeV. The e+e− and μ+μ− decay channels are used to measure the cross section as a function of the rapidity of the J/ψ in the range −2.5<y<2.7, corresponding to an energy in the γp centre-of-mass in the interval 40<Wγp<550 GeV. The measurements, which are consistent with a power law dependence of the exclusive J/ψ photoproduction cross section, are compared to previous results from HERA and the LHC and to several theoretical models. They are found to be compatible with previous measurements.