Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with Nf=2+1 dynamical quark flavors and mπ=200MeV. The s-wave scattering lengths with both total isospins I=1/2 and I=3/2 are inferred from the finite-volume spectrum below the inelastic threshold together with the I=3/2 p-wave containing the Δ(1232) resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels, enabling a determination of the I=3/2 scattering length with statistical errors below 5%, while the I=1/2 scattering length is somewhat less precisely evaluated. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a step toward future computations down to physical light quark masses with multiple lattice spacings and volumes.
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