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admirable n.  and  hoax n.

First numbers that belong to both sets:

84, 234, 308, 364, 438, 476, 644, 650, 654, 762, 1086, 1148, 1484, 1626, 1708, 1842, 1876, 3138, 3164, 3246, 3556, 3836, 3892, 4228, 4396, 4564, 4676, 4844, 4974, 5068, 5298, 5348, 5946, 6054, 6244, 6356, 6524, 6692, 6702, 7026, 7028, 7196, 7364, 7674, 7756, 7782, 7924, 8415, 8754, 9294, 9436, 9716, 9772, 9942, 10698, 10806, 11228, 12068, 12318, 12796, 12908, 12964, 13506, 13748, 14046, 14084, 14644, 15018, 15126, 15148, 15558, 15596, 15764, 15882, 16098, 16746, 17164, 17276, 17718, 17826, 18284, 18474, 18508, 18844, 18956, 19348, 19554, 19852, 21066, 21498, 22708, 23658, 23884, 23996, 24306, 24668, 24954, 25396, 25508, 26348, 26682, 26684, 27188, 27546, 27748, 28252, 28532, 29092, 29166, 29372, 29706, 29932, 30138, 30548, 31276, 31444, 32228, 32284, 32564, 33068, 33378, 33486, 33918, 34076, 34244, 34458, 34636, 34972, 35538, 35756, 35924, 36148, 36932, 37156, 37374, 37482, 38108, 38238, 38276, 38444, 38562, 39318, 39426, 39452, 39642, 40398, 40628, 40684, 40938, 41188, 41468, 42308, 42644, 42774, 43484, 43854, 43876, 45164, 45366, 45556, 45836, 46338, 46396, 46446, 46564, 46676, 47852, 47958, 48244, 48524, 48916, 49084, 49146, 49254, 49756, 49902, 49924, 50428, 50658, 50708, 50766, 51268, 51738, 51846, 52278, 52386, 52388, 52818, 52926, 53228, 53396, 53564, 54006, 54068, 54546, 54628, 54654, 54762, 55086, 56058, 56812, 57092, 57894, 57932, 58324, 58326, 58436, 58492, 58772, 58974, 59298, 59406, 59612, 59838, 60054, 60284, 60508, 60594, 62636, 62692, 62754, 62804, 62862, 63028, 63476, 63644, 63834, 63942, 64374, 64652, 65324, 65346, 65454, 65492, 65716, 66556, 66724, 66892, 67182, 67722, 68236, 68516, 68802, 68852, 69076, 69244, 69356, 70084, 70206, 70962, 71178, 71428, 71596, 71718, 71826, 72042, 72548, 72582, 73276, 73662, 73724, 74396, 74564, 74742, 74956, 75282, 75714, 75822, 76794, 76972, 77084, 77118, 77442, 77476, 77756, 77874, 78148, 78932, 79062, 79324.

Some larger examples :