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admirable n.  and  untouchable n.

First numbers that belong to both sets:

88, 120, 246, 426, 474, 498, 836, 894, 1002, 1074, 1146, 1148, 1266, 1316, 1398, 1506, 1542, 1578, 1758, 1842, 1866, 1888, 1986, 2022, 2118, 2212, 2324, 2454, 2514, 2586, 2766, 2828, 2874, 2922, 2946, 2994, 2996, 3018, 3126, 3246, 3378, 3556, 3642, 3786, 3954, 4062, 4098, 4172, 4206, 4396, 4506, 4614, 4782, 4854, 4926, 4962, 5034, 5142, 5178, 5286, 5322, 5456, 5514, 5908, 6186, 6234, 6294, 6366, 6546, 6774, 6906, 7158, 7192, 7206, 7302, 7364, 7374, 7422, 7554, 7662, 7734, 7782, 7912, 7962, 8166, 8202, 8204, 8394, 8562, 8634, 8706, 8826, 8876, 8886, 8922, 9066, 9268, 9318, 9354, 9402, 9642, 9714, 9716, 9822, 10002, 10158, 10326, 10398, 10446, 10554, 10612, 10662, 10722, 11082, 11166, 11202, 11226, 11406, 11408, 11442, 11452, 11478, 11586, 11694, 11838, 12068, 12234, 12318, 12486, 12522, 12594, 12666, 12796, 12846, 13074, 13076, 13278, 13326, 13506, 13686, 13736, 13972, 14142, 14286, 14334, 14384, 14394, 14466, 14502, 14588, 14682, 14802, 14862, 15126, 15148, 15186, 15258, 15294, 15342, 15654, 15702, 15872, 15932, 15942, 15978, 16122, 16266, 16374, 16446, 16518, 16734, 16772, 16782, 16806, 17058, 17106, 17142, 17166, 17272, 17274, 17276, 17382, 17562, 17634, 17668, 17718, 17742, 17814, 17994, 18066, 18116, 18138, 18222, 18246, 18284, 18366, 18474, 18498, 18534, 18654, 18956, 18978, 19218, 19326, 19626, 20058, 20082, 20154, 20226, 20742, 20766, 20802, 20804, 21028, 21426, 21642, 21786, 22026, 22036, 22206, 22254, 22314, 22316, 22566, 22602, 22782, 22926, 23106, 23156, 23178, 23262, 23286, 23442, 23492, 23502, 23574, 23658, 23682, 24006, 24042, 24164, 24294, 24384, 24438, 24546, 24556, 24666, 24668, 24762, 24798, 24834, 24836, 24942, 25206, 25266, 25396, 25508, 25518, 25554, 25626, 25698, 25782, 26382, 26454, 26526, 26646, 26886, 26958, 27102, 27356, 27524, 27546, 27822, 27858, 27916, 27978, 28218, 28252, 28326, 28364.

Some larger examples :