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palindromic n.  and  pernicious n.

First numbers that belong to both sets:

3, 5, 6, 7, 9, 11, 22, 33, 44, 55, 66, 88, 121, 131, 151, 161, 171, 181, 191, 242, 262, 272, 292, 313, 333, 434, 454, 484, 494, 505, 515, 535, 545, 555, 565, 575, 595, 626, 656, 666, 696, 707, 727, 737, 747, 757, 787, 818, 838, 868, 878, 919, 929, 939, 949, 979, 1001, 1221, 1441, 1881, 2002, 2112, 2332, 2442, 2552, 2882, 3113, 3223, 3333, 3553, 4004, 4114, 4224, 4334, 4664, 4884, 4994, 5005, 5665, 6226, 6446, 6556, 6666, 6776, 6996, 7337, 7557, 7777, 8008, 8228, 8448, 8558, 8668, 8778, 9229, 9449, 9669, 9779, 10301, 10401, 10501, 10601, 10901, 11411, 11711, 11811, 12221, 12421, 12521, 12621, 12721, 13831, 14341, 14441, 14641, 15551, 15851, 16061, 16361, 16461, 16561, 16661, 16761, 17971, 18481, 19091, 19391, 19591, 20102, 20502, 20602, 20802, 20902, 21012, 21112, 21312, 21412, 21612, 21812, 21912, 22522, 22822, 22922, 23332, 23432, 23832, 24442, 24842, 25352, 25552, 26162, 26962, 27472, 27872, 27972, 28382, 28682, 28882, 29092, 29192, 29392, 29692, 29892, 29992, 30303, 30703, 31213, 32223, 32423, 32623, 33133, 33733, 33833, 34243, 34343, 34443, 35553, 35653, 35953, 36163, 36363, 36863, 37173, 37273, 37573, 37673, 37973, 38083, 38383, 38983, 39193, 39493, 40104, 40204, 41414, 41614, 42024, 42224, 42324, 42524, 42624, 42824, 43234, 43334, 43534, 44144, 44544, 45054, 45254, 45354, 45954, 46164, 46664, 46864, 47174, 47874, 48884, 49094, 49194, 49394, 49494, 49694, 49794, 49994, 50205, 50305, 50505, 51215, 52225, 52725, 52925, 53135, 53635, 54145, 54345, 54545, 55155, 55555, 56065, 56565, 57275, 57875, 58885, 59095, 59195, 60606, 60906, 61116, 61416, 61516, 61616, 61716, 62326, 62426, 62926, 63436, 63536, 64346, 64446, 64746, 64846, 64946, 65256, 65356, 65456, 65556, 65656, 65856, 65956, 66166, 66266, 66766, 66966, 67276, 67476, 67876, 67976, 68186, 68486, 68686.

Some larger examples :