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economical n.  and  untouchable n.

First numbers that belong to both sets:

2, 5, 146, 162, 448, 768, 896, 1046, 1134, 1162, 1168, 1186, 1246, 1296, 1312, 1318, 1346, 1418, 1438, 1522, 1538, 1642, 1682, 1718, 1728, 1766, 1774, 1822, 1838, 1888, 1894, 1920, 1922, 1944, 2048, 2058, 2304, 2430, 2432, 2500, 2944, 3008, 3072, 3104, 3136, 3328, 3402, 3430, 3888, 3904, 4480, 4672, 5184, 5376, 5488, 5832, 7168, 7424, 7680, 8000, 8704, 8960, 8978, 9088, 9728, 10006, 10016, 10022, 10066, 10078, 10118, 10198, 10238, 10240, 10294, 10342, 10352, 10366, 10368, 10448, 10496, 10522, 10528, 10544, 10646, 10702, 10752, 10762, 10766, 10798, 10814, 10822, 10880, 10898, 11008, 11014, 11042, 11136, 11146, 11168, 11182, 11236, 11326, 11338, 11360, 11366, 11378, 11422, 11456, 11488, 11502, 11584, 11602, 11606, 11662, 11664, 11686, 11714, 11738, 11774, 11806, 11826, 11846, 11854, 11872, 11998, 12000, 12032, 12082, 12096, 12128, 12134, 12182, 12224, 12250, 12288, 12368, 12418, 12448, 12608, 12718, 12752, 12866, 12928, 12938, 12992, 13056, 13120, 13136, 13138, 13142, 13182, 13216, 13258, 13318, 13358, 13474, 13522, 13582, 13586, 13608, 13632, 13646, 13720, 13742, 13744, 13750, 13778, 13814, 13824, 13856, 13952, 13958, 14016, 14048, 14062, 14078, 14128, 14158, 14192, 14242, 14272, 14318, 14336, 14418, 14486, 14512, 14528, 14576, 14662, 14752, 14864, 14884, 14902, 14962, 14978, 14992, 15008, 15118, 15146, 15154, 15168, 15182, 15206, 15214, 15232, 15286, 15296, 15298, 15382, 15398, 15406, 15424, 15488, 15518, 15536, 15712, 15744, 15754, 15778, 15866, 15872, 15968, 15986, 16000, 16018, 16022, 16078, 16118, 16138, 16162, 16174, 16288, 16358, 16462, 16464, 16526, 16546, 16586, 16672, 16754, 16768, 16774, 16778, 16838, 16854, 16862, 16896, 17002, 17026, 17088, 17150, 17152, 17216, 17246, 17266, 17282, 17312, 17338, 17426, 17438, 17462, 17482, 17496, 17504, 17506, 17558, 17606, 17638, 17678, 17696, 17728, 17734, 17846, 17920, 17938, 18002, 18022, 18058, 18086.

Some larger examples :