In this paper we report two simple relations of masses between corresponding mirror nuclei, the first of which is based on the regularity of empirical neutron-proton interactions, and the second of which is based on the regularity of the one-nucleon separation energy. We demonstrate that, for N >= 10, the empirical neutron-proton interaction of given nucleus with neutron number N - 1 and proton number Z (we use the convention that N = Z in this paper), or abbreviated by the (N - 1, Z) nucleus, equals the neutron-proton interaction of its corresponding mirror nucleus, i.e., the (N, Z - 1) nucleus; we also demonstrate that one-proton separation energy S-p and one-neutron separation energy S-n of the (N - k, Z) nucleus (k = 1, 2, 3, 4) equals one-neutron separation energy S-n and one-proton separation energy S-p, respectively, of the (N, Z - k) nucleus, after a simple correction of Coulomb energy and proton-neutron mass difference are considered. Numerical experiments show that these correlations provide us with a remarkably accurate approach to predict masses and separation energies of some proton-rich nuclei with neutron numbers from 10-46. Our predicted masses of proton-rich nuclei are tabulated as a Supplemental Material of this paper.
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