Most short intervals of length X^theta (theta > 2/15 + eps) contain asymptotically h integers of the form p + a with p prime and a in the lacunary set A_lambda(X).
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Short intervals for the Romanoff-type sumset
Most short intervals of length X^theta (theta > 2/15 + eps) contain asymptotically h integers of the form p + a with p prime and a in the lacunary set A_lambda(X).