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lucky n.  and  plaindrome

First numbers that belong to both sets:

1, 3, 7, 9, 13, 15, 25, 33, 37, 49, 67, 69, 79, 99, 111, 115, 127, 129, 133, 135, 159, 169, 189, 223, 235, 237, 259, 267, 289, 339, 349, 357, 367, 399, 477, 489, 559, 577, 579, 679, 699, 777, 1117, 1123, 1147, 1155, 1167, 1179, 1189, 1233, 1245, 1249, 1339, 1357, 1369, 1389, 1455, 1459, 1567, 1579, 1599, 1777, 1899, 2239, 2257, 2277, 2335, 2355, 2379, 2445, 2467, 2479, 2557, 2589, 2599, 2667, 2689, 2899, 3339, 3355, 3477, 3489, 3499, 3559, 3579, 3669, 3789, 3889, 3999, 4455, 4567, 4569, 4699, 4999, 5559, 5569, 5577, 5589, 5599, 5679, 5889, 6667, 6669, 6679, 6789, 6999, 7779, 7899, 9999, 11113, 11137, 11157, 11223, 11227, 11239, 11245, 11247, 11259, 11269, 11289, 11377, 11389, 11479, 11577, 11599, 11667, 11677, 11679, 12223, 12237, 12267, 12333, 12337, 12357, 12379, 12399, 12457, 12499, 12567, 12579, 12589, 12679, 12699, 12777, 12799, 12999, 13335, 13345, 13347, 13359, 13489, 13567, 13599, 13677, 14449, 14457, 14599, 14667, 14689, 14779, 14899, 15567, 15577, 16677, 22225, 22227, 22269, 22333, 22339, 22369, 22377, 22399, 22479, 22555, 22569, 22689, 22779, 22789, 22999, 23355, 23377, 23445, 23449, 23457, 23469, 23479, 23499, 23569, 23577, 23677, 23689, 23799, 23889, 24447, 24499, 24669, 24789, 25567, 25569, 25677, 33333, 33337, 33349, 33379, 33445, 33567, 34449, 34557, 34569, 34599, 34777, 35557, 35577, 35799, 36669, 36679, 37789, 44499, 44889, 45555, 45789, 46999, 47799, 47889, 48999, 55555, 55569, 56679, 56779, 56799, 56899, 57777, 57889, 58999, 66667, 66669, 66699, 67899, 69999, 111111, 111115, 111123, 111169, 111177, 111237, 111259, 111267, 111337, 111355, 111469, 111489, 111499, 111589, 111667, 111777, 111999, 112227, 112239, 112245, 112257, 112339, 112459, 112479, 112689, 112699, 113379, 113445, 113455, 113469, 113559, 113569, 113689, 113799, 113889, 114477, 114579, 114589, 114669, 114789, 114999.

Some larger examples :