Search a number
hoax n.  and  untouchable n.

First numbers that belong to both sets:

336, 516, 562, 732, 1116, 1148, 1312, 1404, 1642, 1650, 1822, 1842, 1894, 2008, 2218, 2232, 2356, 2500, 2614, 2640, 2760, 2902, 3036, 3246, 3476, 3484, 3556, 3592, 3630, 3792, 4116, 4148, 4188, 4198, 4268, 4344, 4396, 4770, 4980, 5094, 5386, 5458, 5602, 6060, 6178, 6184, 6502, 6596, 6904, 7062, 7364, 7402, 7428, 7782, 7850, 8284, 8334, 8508, 8724, 8790, 8816, 8982, 9028, 9116, 9180, 9382, 9412, 9716, 10044, 10192, 10240, 10278, 10406, 11232, 11574, 11686, 11688, 11774, 12068, 12318, 12464, 12532, 12558, 12796, 12828, 12880, 12932, 12952, 13194, 13296, 13428, 13506, 13520, 13560, 13588, 14076, 14242, 14268, 14472, 14476, 14484, 14712, 14946, 14962, 14980, 15024, 15126, 15148, 15168, 15256, 15282, 15286, 15356, 15712, 15780, 15786, 15950, 16000, 16078, 16348, 16546, 16684, 16752, 16770, 17150, 17276, 17364, 17482, 17556, 17616, 17718, 17964, 18022, 18032, 18058, 18284, 18418, 18474, 18612, 18742, 18836, 18850, 18956, 19168, 19308, 19316, 19516, 19550, 19708, 20208, 20516, 20542, 20660, 20970, 20974, 21226, 21262, 21268, 21584, 21828, 21942, 22086, 22144, 22342, 22386, 22508, 22518, 22608, 22736, 23196, 23658, 23850, 23908, 24068, 24128, 24142, 24352, 24480, 24620, 24668, 24676, 24732, 25000, 25006, 25132, 25298, 25396, 25484, 25508, 25560, 25950, 26256, 26302, 26946, 27036, 27236, 27516, 27546, 27548, 27562, 27660, 27684, 27840, 27892, 28252, 28348, 28384, 28532, 28564, 28680, 29092, 29372, 29398, 29542, 29660, 29712, 29758, 29902, 29938, 30056, 30088, 30548, 30564, 30658, 30696, 30750, 30788, 30802, 30834, 30926, 31228, 31376, 31598, 31740, 31746, 32188, 32226, 32228, 32278, 32392, 32458, 32484, 32528, 32638, 32962, 33090, 33336, 33436, 33486, 33712, 33764, 33862, 33900, 34048, 34076, 34188, 34452, 34582, 34636, 34928, 34960, 34972, 35188, 35350, 35490, 35636, 35874, 35878, 36036, 36382, 36522, 36720, 36804, 37156, 37462, 37606, 37894, 38002, 38008, 38160.

Some larger examples :