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Moran n.  and  untouchable n.

First numbers that belong to both sets:

372, 516, 518, 732, 738, 804, 1168, 1236, 1746, 1896, 1962, 2022, 2316, 2608, 2718, 3982, 4086, 4336, 4842, 5094, 6064, 6282, 6310, 6352, 6462, 6606, 6822, 7146, 7944, 8110, 8334, 8622, 10232, 10278, 10308, 10386, 10968, 11202, 11358, 11574, 11606, 11646, 11688, 11710, 12294, 12762, 13194, 13374, 14126, 14128, 14166, 14568, 14922, 15426, 16210, 16542, 16580, 16584, 16722, 17008, 17668, 18238, 19242, 20028, 20312, 20316, 20464, 20934, 21036, 22332, 22662, 23410, 23412, 23702, 23928, 24714, 24792, 25030, 25072, 25182, 25362, 25366, 25614, 25902, 26088, 26118, 26222, 26512, 27638, 27672, 28062, 28206, 28422, 29142, 29544, 30506, 30582, 30612, 30696, 30762, 31002, 31112, 31116, 31446, 31554, 31662, 32018, 32098, 32124, 32166, 32418, 32788, 32814, 33246, 33822, 34326, 35042, 35622, 36306, 36522, 36896, 37460, 37602, 38616, 39222, 39912, 40048, 40116, 40518, 40776, 40806, 40914, 41166, 41274, 41346, 41562, 41784, 42138, 42318, 42936, 43182, 43504, 43506, 44046, 44406, 44808, 45702, 46358, 46422, 46824, 47106, 47540, 50454, 50704, 51318, 51822, 52144, 52872, 53154, 54342, 54744, 55312, 55462, 55464, 55602, 56142, 56654, 56988, 57006, 57990, 58526, 59060, 59398, 59462, 59790, 59868, 60132, 60174, 60462, 60714, 61038, 61326, 61368, 62334, 62442, 62512, 63306, 63702, 63968, 64062, 64536, 65078, 65362, 65696, 66114, 66260, 66408, 66848, 66996, 67128, 67966, 68022, 68424, 68576, 68578, 68790, 68868, 69588, 69728, 70212, 70542, 70580, 70722, 71152, 71406, 71660, 72018, 72566, 73282, 74322, 74502, 74616, 74988, 75842, 77060, 77758, 77790, 77796, 78072, 79224, 79668, 79956, 80118, 80226, 80334, 80402, 81126, 81384, 82684, 82862, 82976, 84620, 84990, 85014, 85128, 85708, 85788, 87432, 89236, 90162, 90414, 90456, 90702, 91752, 92142, 92328, 92472, 93006, 93158, 93222, 94056, 94496, 94632, 95208, 96072, 96870, 96948, 97596, 97770, 97952, 98308, 99390, 99570, 101316, 101718, 101754, 101862, 102326, 103374, 103482.

Some larger examples :