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nude n.  and  pernicious n.

First numbers that belong to both sets:

3, 5, 6, 7, 9, 11, 12, 22, 24, 33, 36, 44, 48, 55, 66, 88, 112, 115, 122, 124, 132, 144, 155, 162, 168, 224, 244, 248, 264, 288, 324, 333, 336, 384, 412, 448, 488, 515, 555, 648, 666, 672, 728, 784, 824, 936, 1113, 1116, 1144, 1184, 1222, 1236, 1288, 1296, 1311, 1332, 1335, 1344, 1362, 1368, 1395, 1444, 1448, 1488, 1555, 1715, 1722, 1888, 1962, 2112, 2128, 2144, 2184, 2226, 2232, 2288, 2444, 2616, 2622, 2664, 2688, 2888, 3333, 3393, 3444, 3624, 3816, 3924, 4112, 4116, 4128, 4144, 4164, 4212, 4224, 4288, 4368, 4416, 4464, 4888, 4932, 5155, 5515, 6144, 6312, 6612, 6666, 6696, 6762, 6816, 6888, 7112, 7476, 7777, 7784, 8128, 8224, 8232, 8288, 8328, 8424, 8448, 8616, 8736, 8832, 8928, 9126, 9144, 9162, 9216, 9333, 9864, 11112, 11136, 11172, 11184, 11232, 11262, 11288, 11322, 11424, 11436, 11444, 11448, 11555, 11688, 11711, 11832, 11888, 11916, 12112, 12128, 12162, 12168, 12222, 12224, 12288, 12412, 12488, 12612, 12624, 12636, 12824, 12848, 13224, 13332, 13335, 13377, 13392, 13632, 13644, 13713, 13776, 14128, 14212, 14224, 14444, 16122, 16362, 16416, 16464, 16644, 16662, 16716, 16848, 17248, 17472, 17717, 17724, 17766, 18112, 18184, 18264, 18288, 18384, 18432, 18448, 18488, 18824, 18848, 18872, 19116, 19368, 19719, 19935, 21112, 21122, 21124, 21128, 21162, 21184, 21224, 21264, 21312, 21324, 21336, 21412, 21424, 21444, 21448, 21612, 21624, 21636, 21648, 21816, 21824, 21848, 21864, 21888, 21924, 22116, 22128, 22144, 22164, 22184, 22212, 22224, 22344, 22368, 22416, 22464, 22644, 22848, 22888, 22896, 22932, 23124, 23316, 23364, 23616, 23622, 23664, 23832, 24112, 24132, 24144, 24224, 24324, 24336, 24384, 24444, 24448, 24724, 24824, 24912, 26436, 26448, 26664, 26964, 27412, 27972, 28184, 28296, 28424, 28448, 28888, 28944, 29124, 29322, 31266.

Some larger examples :