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odious n.  and  plaindrome

First numbers that belong to both sets:

1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 22, 25, 26, 28, 35, 37, 38, 44, 47, 49, 55, 56, 59, 67, 69, 79, 88, 112, 115, 117, 118, 122, 124, 127, 128, 133, 134, 137, 138, 145, 146, 148, 155, 157, 158, 167, 168, 179, 188, 199, 223, 224, 227, 229, 233, 234, 236, 239, 244, 247, 248, 256, 259, 266, 268, 279, 289, 299, 333, 334, 336, 339, 345, 346, 348, 355, 357, 358, 367, 369, 379, 388, 445, 446, 448, 457, 458, 466, 468, 477, 478, 488, 499, 555, 557, 558, 566, 569, 577, 578, 589, 666, 668, 677, 678, 689, 699, 779, 789, 799, 889, 899, 1113, 1114, 1116, 1119, 1123, 1125, 1126, 1129, 1135, 1137, 1138, 1144, 1147, 1149, 1156, 1159, 1166, 1168, 1177, 1178, 1189, 1199, 1222, 1225, 1226, 1228, 1233, 1234, 1236, 1239, 1245, 1246, 1249, 1255, 1256, 1259, 1267, 1269, 1279, 1288, 1299, 1335, 1336, 1339, 1344, 1347, 1349, 1356, 1359, 1367, 1368, 1377, 1378, 1389, 1444, 1447, 1448, 1456, 1459, 1466, 1468, 1479, 1488, 1555, 1557, 1558, 1567, 1568, 1577, 1578, 1588, 1667, 1669, 1679, 1688, 1777, 1778, 1789, 1888, 1999, 2223, 2225, 2226, 2228, 2235, 2237, 2238, 2245, 2246, 2249, 2255, 2257, 2258, 2267, 2269, 2279, 2288, 2335, 2336, 2339, 2345, 2346, 2348, 2356, 2359, 2366, 2368, 2377, 2378, 2388, 2444, 2447, 2449, 2455, 2456, 2459, 2466, 2468, 2477, 2478, 2489, 2555, 2557, 2558, 2567, 2568, 2579, 2588, 2667, 2669, 2677, 2678, 2688, 2777, 2778, 2789, 2799, 2888, 2899, 2999, 3333, 3334, 3337, 3338, 3345, 3346, 3348, 3355, 3357, 3358, 3367, 3368, 3379, 3388, 3399, 3444, 3447, 3448, 3457, 3458, 3467, 3469, 3477, 3478, 3488, 3556, 3559, 3566.

Some larger examples :