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evil n.  and  palindromic n.

First numbers that belong to both sets:

3, 5, 6, 9, 33, 66, 77, 99, 101, 111, 141, 202, 212, 222, 232, 252, 272, 282, 303, 323, 343, 353, 363, 373, 383, 393, 404, 414, 424, 444, 464, 474, 525, 585, 606, 616, 636, 646, 676, 686, 717, 777, 797, 808, 828, 848, 858, 888, 898, 909, 969, 989, 999, 1111, 1331, 1551, 1661, 1771, 1991, 2112, 2222, 2662, 2772, 2992, 3443, 3663, 3883, 3993, 4224, 4444, 4554, 4774, 5115, 5225, 5335, 5445, 5555, 5775, 5885, 6116, 6336, 6886, 7007, 7227, 7447, 7667, 7887, 7997, 8118, 8338, 8448, 8888, 8998, 9009, 9339, 9559, 9889, 9999, 10001, 10701, 10801, 11011, 11311, 11511, 11911, 12021, 12321, 12821, 12921, 13131, 13231, 13331, 13631, 13731, 14141, 14241, 14541, 14741, 14841, 15151, 15351, 15651, 15951, 16161, 16861, 16961, 17071, 17171, 17471, 17571, 17671, 17771, 18081, 18181, 18281, 18581, 18681, 18781, 18881, 18981, 19191, 19491, 19991, 20002, 20702, 21212, 21512, 21712, 22022, 22122, 22322, 22622, 22722, 23132, 23232, 23532, 23632, 23732, 23932, 24042, 24542, 24642, 24742, 24942, 25052, 25152, 25252, 25452, 25652, 25752, 25952, 26262, 26362, 26462, 26562, 26662, 26762, 27072, 27172, 27272, 27672, 28182, 28282, 28482, 28582, 28782, 28982, 29292, 29492, 29592, 29792, 30103, 30203, 30503, 30603, 30803, 30903, 31013, 31113, 31313, 31413, 31613, 31713, 31813, 32023, 32123, 32523, 32723, 32823, 32923, 33033, 33233, 33333, 33433, 33633, 33933, 34543, 34643, 34743, 34843, 35053, 35153, 35253, 35353, 35753, 35853, 36063, 36463, 36663, 36763, 36963, 37073, 37373, 37473, 37773, 38183, 38283, 38483, 38583, 38783, 38883, 39093, 39293, 39393, 39593, 39693, 39893, 39993, 40004, 40304, 40504, 40704, 41014, 41114, 41314, 41514, 41714, 41814, 42124, 42424, 42724, 43034, 43434, 43634, 43934, 44044, 44244, 44344, 44644, 44744, 44944, 45154, 45454, 45654, 46264, 46364, 46464, 46964, 47074, 47274.

Some larger examples :