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Moran n.  and  unprimeable n.

First numbers that belong to both sets:

516, 518, 846, 1854, 1896, 1898, 1926, 1962, 2826, 3474, 4065, 4086, 4194, 4776, 4842, 5496, 5962, 6648, 6754, 7146, 7982, 8334, 8338, 8406, 10012, 10014, 10232, 10236, 10386, 10674, 10818, 10926, 10968, 11202, 11530, 11535, 11538, 11604, 11606, 11646, 11754, 12186, 12294, 12362, 13086, 13116, 13118, 13194, 13374, 13404, 13605, 14126, 14128, 14166, 14230, 14704, 15534, 15864, 16326, 16580, 16584, 17008, 17842, 18380, 18475, 18925, 19820, 20312, 20316, 20426, 20464, 21078, 21258, 21366, 21474, 21906, 22266, 22332, 22335, 22958, 23235, 23238, 23344, 23346, 23386, 23526, 23702, 24606, 24714, 24775, 24936, 25614, 25722, 27414, 27925, 28138, 28824, 28825, 29180, 29275, 29544, 30036, 30474, 30546, 30582, 30610, 30612, 31002, 31112, 31116, 31404, 31446, 31554, 32018, 32124, 32166, 32272, 32814, 33130, 33682, 34078, 35004, 35042, 35514, 35622, 35660, 35662, 36054, 37934, 37978, 39175, 39806, 39912, 40048, 40266, 40332, 40335, 40336, 40374, 40912, 40914, 41274, 41562, 41780, 41784, 42246, 42310, 42318, 42426, 43074, 43305, 43504, 43506, 43580, 43675, 43876, 44406, 44664, 45096, 45740, 46005, 46422, 47106, 48264, 48916, 49340, 49568, 50162, 51174, 51318, 52035, 52940, 53154, 53226, 53334, 53575, 53660, 54380, 54456, 54475, 54744, 55422, 55972, 56184, 56186, 56254, 56275, 56328, 56725, 57006, 58340, 58492, 58525, 58526, 59420, 59425, 59936, 60174, 60246, 60405, 60462, 61326, 61434, 62224, 62226, 62334, 62442, 62512, 62575, 63010, 63015, 63306, 63816, 63968, 64026, 64248, 64536, 64825, 65362, 66114, 66260, 66482, 66996, 68424, 68576, 68578, 69588, 69728, 69965, 70212, 70694, 71046, 71406, 72126, 72234, 72456, 72566, 72740, 73026, 73176, 73282, 73314, 73460, 73464, 74540, 74988, 75842, 76054, 76056, 76525, 77758, 78140, 78148, 78216, 79512, 79594, 79956, 80046, 80334, 81126, 81384, 81414, 81475, 82684, 82825, 82862, 82976, 83180, 83188, 83502, 83540, 84114, 85014, 86606, 86796, 88152, 88732, 90380, 90414, 90456.

Some larger examples :