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plaindrome  and  sphenic n.

First numbers that belong to both sets:

66, 78, 114, 138, 222, 238, 246, 255, 258, 266, 345, 357, 366, 399, 455, 555, 678, 777, 1113, 1118, 1146, 1158, 1166, 1178, 1222, 1235, 1239, 1245, 1246, 1258, 1266, 1334, 1335, 1338, 1358, 1378, 1446, 1455, 1479, 1558, 1578, 1599, 1677, 1778, 2222, 2233, 2235, 2238, 2247, 2255, 2266, 2278, 2289, 2334, 2337, 2338, 2345, 2355, 2378, 2379, 2445, 2555, 2666, 2667, 2678, 2679, 2778, 3333, 3335, 3345, 3346, 3355, 3358, 3367, 3378, 3399, 3445, 3477, 3478, 3558, 3567, 3678, 3689, 3999, 4445, 4458, 4558, 4566, 4669, 4899, 5555, 5558, 5559, 5678, 5889, 6789, 7777, 11122, 11134, 11135, 11137, 11139, 11145, 11155, 11158, 11166, 11222, 11226, 11229, 11234, 11238, 11245, 11247, 11258, 11266, 11289, 11334, 11339, 11355, 11446, 11455, 11458, 11478, 11557, 11577, 11578, 11666, 11679, 12234, 12238, 12245, 12257, 12259, 12278, 12334, 12338, 12345, 12355, 12358, 12378, 12445, 12455, 12466, 12467, 12478, 12489, 12566, 12567, 12578, 12579, 12666, 12669, 12678, 12999, 13334, 13345, 13359, 13366, 13447, 13458, 13478, 13489, 13559, 13677, 13678, 13699, 13889, 13899, 14446, 14457, 14466, 14467, 14555, 14558, 14559, 14577, 14578, 14678, 14889, 15558, 15566, 15589, 15789, 15799, 16666, 16678, 16899, 17778, 17799, 17889, 22222, 22227, 22245, 22258, 22269, 22334, 22335, 22345, 22355, 22358, 22359, 22366, 22378, 22379, 22389, 22449, 22466, 22479, 22555, 22557, 22566, 22666, 22778, 22899, 23334, 23335, 23338, 23349, 23359, 23366, 23446, 23457, 23458, 23466, 23555, 23577, 23579, 23777, 23779, 24446, 24447, 24455, 24458, 24459, 24466, 24477, 24479, 24555, 24558, 24566, 24567, 24666, 24679, 24778, 24999, 25555, 25557, 25558, 25566, 25666, 25669, 25678, 25779, 25789, 25899, 26666, 26677, 26778, 26789, 27777, 27789, 33333, 33334, 33335, 33337, 33338, 33355, 33358, 33378, 33446, 33449, 33459, 33466, 33478, 33555, 33566, 33567, 33578, 33677, 33699.

Some larger examples :