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admirable n.  and  apocalyptic n.

First numbers that belong to both sets:

222, 224, 366, 582, 650, 822, 836, 868, 894, 1002, 1086, 1158, 1194, 1316, 1338, 1372, 1374, 1434, 1488, 1578, 1626, 1638, 1652, 1708, 1758, 1866, 2002, 2118, 2202, 2212, 2238, 2274, 2298, 2324, 2382, 2454, 2492, 2586, 2634, 2694, 2716, 2766, 2828, 2874, 2884, 2946, 2994, 2996, 3054, 3126, 3164, 3230, 3246, 3250, 3282, 3342, 3414, 3426, 3462, 3522, 3594, 3668, 3678, 3714, 3770, 3786, 3858, 3882, 3892, 3954, 3966, 4062, 4146, 4206, 4254, 4396, 4398, 4458, 4506, 4542, 4566, 4614, 4638, 4676, 4722, 4782, 4854, 4866, 4962, 4974, 5012, 5034, 5068, 5118, 5142, 5178, 5286, 5298, 5322, 5348, 5442, 5456, 5466, 5514, 5516, 5572, 5574, 5622, 5624, 5646, 5682, 5718, 5802, 5826, 5830, 5862, 5898, 5908, 5982, 6078, 6114, 6126, 6186, 6198, 6200, 6234, 6244, 6356, 6366, 6378, 6412, 6414, 6435, 6522, 6546, 6582, 6618, 6654, 6692, 6702, 6738, 6748, 6774, 6906, 6918, 6978, 7026, 7028, 7086, 7122, 7196, 7206, 7278, 7302, 7338, 7364, 7386, 7422, 7425, 7494, 7532, 7554, 7588, 7674, 7698, 7734, 7746, 7756, 7782, 7806, 7818, 7868, 7912, 7914, 7924, 7926, 7962, 8166, 8202, 8204, 8238, 8286, 8394, 8415, 8432, 8454, 8538, 8562, 8596, 8598, 8634, 8682, 8706, 8708, 8718, 8754, 8764, 8826, 8876, 8898, 8922, 8925, 8934, 8958, 8994, 9066, 9112, 9138, 9186, 9258, 9294, 9318, 9354, 9402, 9424, 9426, 9436, 9474, 9498, 9555, 9582, 9606, 9642, 9654, 9678, 9714, 9716, 9726, 9762, 9772, 9822, 9884, 9942, 9978, 10002, 10014, 10052, 10158, 10182, 10194, 10254, 10326, 10338, 10398, 10444, 10446, 10518, 10554, 10612, 10662, 10698, 10722, 10724, 10734, 10792, 10806, 10866, 10892, 10938, 10986, 11082, 11096, 11116, 11166, 11202, 11226, 11228, 11238, 11262, 11274, 11334, 11406, 11408, 11442, 11452, 11478, 11586, 11598, 11694, 11706.

Some larger examples :