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odious n.  and  Smith n.

First numbers that belong to both sets:

4, 22, 94, 121, 265, 274, 319, 346, 355, 382, 391, 454, 517, 535, 648, 654, 666, 690, 728, 762, 852, 861, 895, 913, 985, 1165, 1219, 1255, 1282, 1284, 1507, 1633, 1736, 1795, 1822, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1952, 1962, 2038, 2173, 2218, 2286, 2326, 2366, 2373, 2461, 2475, 2515, 2576, 2688, 2722, 2745, 2751, 2839, 2888, 2902, 2911, 2958, 2965, 2970, 3091, 3246, 3258, 3345, 3442, 3505, 3649, 3690, 3865, 3973, 4054, 4126, 4162, 4173, 4185, 4191, 4198, 4209, 4279, 4306, 4414, 4428, 4464, 4557, 4594, 4702, 4765, 4794, 4832, 4855, 4918, 4954, 4959, 4960, 5062, 5071, 5172, 5242, 5248, 5253, 5305, 5386, 5388, 5422, 5526, 5539, 5602, 5638, 5642, 5854, 5926, 5935, 5998, 6036, 6084, 6096, 6115, 6188, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6583, 6702, 6816, 6934, 6981, 7136, 7186, 7195, 7287, 7438, 7465, 7503, 7627, 7712, 7762, 7764, 7784, 8014, 8077, 8095, 8158, 8185, 8257, 8277, 8372, 8518, 8545, 8653, 8736, 8754, 8766, 8792, 8883, 9031, 9229, 9285, 9387, 9427, 9535, 9571, 9598, 9684, 9717, 9968, 9985, 10201, 10296, 10419, 10494, 10579, 10592, 10698, 10705, 10736, 10761, 10786, 10791, 10797, 10806, 10887, 11696, 11790, 11857, 11984, 12055, 12406, 12573, 12622, 12627, 12658, 12667, 12939, 12975, 13369, 13454, 13472, 13662, 13666, 13747, 13764, 13812, 13905, 14017, 14058, 14085, 14148, 14179, 14206, 14359, 14422, 14508, 14534, 14719, 14756, 14809, 14924, 14946, 14958, 14985, 14991, 15128, 15205, 15646, 15682, 15687, 15835, 15848, 15853, 15882, 15884, 15943, 15974, 16098, 16192, 16222, 16285, 16357, 16438, 16474, 16480, 16537, 16568, 16582, 16591, 16647, 16653, 16744, 16940, 16983, 17149, 17238, 17268, 17271, 17424, 17455, 17482, 17496, 17635, 17662, 17664, 17698, 17718, 17754, 17833, 17885, 17889, 17907, 17916.

Some larger examples :