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apocalyptic n.  and  plaindrome

First numbers that belong to both sets:

157, 222, 224, 226, 245, 247, 278, 355, 366, 478, 499, 578, 666, 667, 669, 1128, 1133, 1135, 1136, 1138, 1139, 1155, 1157, 1158, 1166, 1199, 1224, 1245, 1246, 1247, 1257, 1259, 1267, 1277, 1279, 1289, 1333, 1338, 1339, 1345, 1347, 1349, 1359, 1399, 1449, 1466, 1467, 1468, 1478, 1488, 1499, 1556, 1568, 1578, 1588, 1589, 1666, 1667, 1669, 1679, 1688, 1777, 1889, 1899, 2222, 2223, 2224, 2225, 2226, 2227, 2229, 2234, 2238, 2239, 2245, 2246, 2247, 2259, 2267, 2269, 2277, 2278, 2279, 2333, 2335, 2344, 2345, 2346, 2347, 2348, 2349, 2356, 2358, 2359, 2366, 2368, 2378, 2388, 2389, 2399, 2445, 2446, 2447, 2448, 2449, 2466, 2467, 2469, 2477, 2479, 2489, 2557, 2566, 2569, 2579, 2588, 2589, 2668, 2669, 2677, 2678, 2679, 2699, 2789, 2899, 3333, 3334, 3336, 3338, 3339, 3346, 3348, 3355, 3356, 3358, 3366, 3367, 3368, 3369, 3377, 3379, 3388, 3389, 3444, 3445, 3446, 3447, 3448, 3459, 3467, 3469, 3478, 3488, 3555, 3557, 3559, 3566, 3569, 3577, 3578, 3579, 3588, 3667, 3668, 3677, 3678, 3688, 3689, 3699, 3778, 3788, 3789, 3799, 3888, 3889, 3899, 4447, 4449, 4455, 4456, 4457, 4458, 4459, 4467, 4468, 4488, 4555, 4556, 4557, 4558, 4559, 4566, 4567, 4568, 4577, 4578, 4579, 4588, 4589, 4599, 4666, 4667, 4668, 4669, 4677, 4678, 4679, 4688, 4689, 4699, 4778, 4779, 4788, 4789, 4799, 4888, 4889, 4899, 4999, 5555, 5557, 5558, 5559, 5566, 5568, 5569, 5578, 5579, 5588, 5589, 5669, 5678, 5679, 5688, 5689, 5699, 5777, 5788, 5799, 5888, 5889, 5899, 5999, 6666, 6667, 6668, 6677, 6678, 6688, 6699, 6777, 6778, 6779, 6788, 6889, 6899, 7777, 7778, 7779, 7788, 7789, 7799, 7888, 7899, 7999, 8899, 8999, 9999, 11111, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119, 11122, 11123, 11124.

Some larger examples :