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Four dimensional N = 1 supersymmetrization of R 4 in superspace

We write an action, in four dimensional N = 1 curved superspace, which contains a pure R 4 term with a coupling constant. Starting from the off-shell solution of the Bianchi identities, we compute the on-shell torsions and curvatures with this term. We show that their complete solution includes, for some of them, an infinite series in the R 4 coupling constant, which can only be computed iteratively. We explicitly compute the superspace tor-sions and curvatures up to second order in this coupling constant. Finally, we comment on the lifting of this result to higher dimensions.