We present a lattice QCD study of N pi scattering in the positive-parity nucleon channel, where the puzzling Roper resonance N*(1440) resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with N-f = 2 + 1 Wilson-clover dynamical fermions, m pi similar or equal to 156 MeV and L similar or equal to 2.9 fm. In addition to a number of qqq interpolating fields, we implement operators for N pi in p-wave and N sigma in s-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by N(0), N(0) pi(0)pi(0) [mixed with N(0)sigma(0)] and N(p)pi(-p) with p similar or equal to 2 pi/L, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental Np phase shift would-in the approximation of purely elastic Np scattering-imply an additional eigenstate near the Roper mass m(R) similar or equal to 1.43 GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that N pi elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with N pi pi, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of the previous lattice studies based just on qqq interpolators, which did not find a Roper eigenstate below 1.65 GeV. The study of the coupled-channel scattering including a three-particle decay N pi pi remains a challenge.