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nude n.  and  untouchable n.

First numbers that belong to both sets:

2, 5, 88, 124, 162, 216, 248, 288, 324, 336, 448, 612, 624, 784, 848, 936, 1116, 1128, 1212, 1222, 1236, 1248, 1266, 1288, 1296, 1326, 1332, 1632, 1692, 1888, 1944, 1962, 2128, 2136, 2196, 2212, 2226, 2232, 2248, 2262, 2316, 2322, 2364, 2436, 2824, 3126, 3132, 3144, 3162, 3276, 3312, 3366, 3384, 3432, 3636, 3648, 3666, 3816, 3888, 4116, 4172, 4184, 4224, 4248, 4344, 4368, 4416, 4488, 4896, 6168, 6216, 6366, 6384, 6624, 6816, 6966, 7266, 7476, 7784, 8136, 8184, 8328, 8488, 8496, 8616, 8688, 8848, 9126, 9144, 9216, 9648, 9864, 11136, 11166, 11196, 11226, 11232, 11248, 11316, 11364, 11436, 11488, 11616, 11664, 11688, 11872, 12128, 12132, 12168, 12216, 12224, 12248, 12288, 12432, 12444, 12448, 12636, 12666, 12712, 12848, 12888, 13212, 13224, 13248, 13266, 13326, 13362, 13392, 13416, 13632, 13662, 13776, 13824, 14128, 14184, 14232, 14248, 14292, 14436, 14488, 14616, 14664, 14688, 14728, 16116, 16122, 16248, 16266, 16416, 16464, 16626, 16644, 16716, 16848, 16992, 17136, 17262, 17766, 18112, 18216, 18248, 18264, 18336, 18432, 18848, 18936, 19224, 19296, 19332, 19368, 21112, 21168, 21184, 21216, 21264, 21288, 21336, 21424, 21432, 21448, 21636, 21666, 21672, 21784, 21816, 21888, 21924, 22116, 22122, 22144, 22176, 22224, 22236, 22244, 22288, 22332, 22424, 22662, 22824, 22848, 22888, 22896, 22932, 23112, 23166, 23184, 23226, 23232, 23262, 23316, 23364, 23412, 23424, 23436, 23772, 23922, 24128, 24144, 24168, 24192, 24244, 24276, 24312, 24336, 24384, 24412, 24636, 24696, 24816, 24912, 26124, 26136, 26412, 26616, 26832, 27216, 27384, 27636, 27762, 28128, 28144, 28224, 28288, 28344, 28416, 28888, 29322, 29448, 29736, 31116, 31164, 31236, 31344, 31362, 31368, 31416, 31464, 31662, 31896, 32112, 32124, 32136, 32166, 32172, 32226, 32232, 32292, 32316, 32436, 32448, 33216, 33222, 33264, 33336, 33366, 33384, 33432, 33636, 33666, 33696.

Some larger examples :