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alternating n.  and  lucky n.

First numbers that belong to both sets:

1, 3, 7, 9, 21, 25, 43, 49, 63, 67, 69, 87, 105, 127, 129, 141, 163, 169, 189, 303, 307, 321, 327, 349, 361, 367, 385, 529, 541, 583, 723, 727, 729, 741, 745, 769, 781, 787, 903, 925, 927, 961, 981, 2121, 2125, 2127, 2163, 2187, 2301, 2323, 2343, 2365, 2505, 2523, 2527, 2545, 2563, 2587, 2589, 2725, 2763, 2781, 2785, 2787, 2901, 2905, 2923, 2943, 2961, 2983, 4105, 4107, 4129, 4161, 4165, 4189, 4321, 4329, 4363, 4383, 4389, 4509, 4521, 4561, 4567, 4569, 4587, 4725, 4741, 4761, 4767, 4929, 4963, 4965, 4969, 4987, 4989, 6123, 6141, 6147, 6163, 6301, 6309, 6345, 6363, 6367, 6369, 6385, 6501, 6505, 6523, 6541, 6567, 6723, 6741, 6745, 6747, 6763, 6765, 6783, 6787, 6789, 6909, 6921, 6981, 6985, 8107, 8109, 8127, 8161, 8169, 8325, 8347, 8365, 8367, 8583, 8589, 8769, 8787, 8947, 8961, 8989, 10125, 10143, 10147, 10149, 10321, 10341, 10363, 10365, 10387, 10501, 10507, 10509, 10525, 10563, 10569, 10585, 10587, 10723, 10725, 10747, 10785, 10789, 10903, 10909, 10921, 10923, 10945, 10965, 12103, 12121, 12141, 12163, 12165, 12301, 12307, 12321, 12363, 12543, 12547, 12567, 12589, 12709, 12729, 12741, 12763, 12781, 12903, 12907, 12925, 12961, 12969, 14163, 14181, 14185, 14307, 14347, 14349, 14367, 14505, 14521, 14523, 14541, 14565, 14587, 14721, 14749, 14785, 14905, 14923, 14943, 14947, 16101, 16309, 16329, 16341, 16365, 16381, 16387, 16389, 16507, 16521, 16701, 16707, 16725, 16747, 16765, 16921, 16947, 16969, 16981, 18123, 18127, 18145, 18147, 18169, 18181, 18187, 18189, 18303, 18381, 18501, 18523, 18543, 18589, 18723, 18745, 18747, 18765, 18783, 18787, 18943, 18967, 18969, 18987, 30103, 30121, 30163, 30181, 30303, 30327, 30367, 30369, 30387, 30505, 30523, 30529, 30541, 30543, 30547, 30565, 30567, 30589, 30727, 30747, 30765, 30789, 30901, 30943.

Some larger examples :