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equidigital n.  and  Moran n.

First numbers that belong to both sets:

21, 27, 111, 133, 201, 511, 1011, 1095, 1101, 1141, 1168, 1185, 1387, 1455, 1659, 1679, 3031, 10095, 10096, 10109, 10213, 10279, 10307, 10346, 10365, 10479, 10543, 10635, 10727, 10901, 10905, 10963, 10983, 11085, 11265, 11354, 11355, 11487, 11535, 11606, 11647, 11805, 11824, 11991, 12165, 12181, 12345, 12362, 12435, 12563, 12747, 12873, 13111, 13118, 13155, 13245, 13264, 13605, 13881, 14055, 14093, 14099, 14128, 14383, 14505, 14704, 14769, 15001, 15267, 15393, 15409, 15519, 15579, 15623, 15689, 15751, 15771, 15775, 15849, 16149, 16389, 16527, 16659, 17283, 17409, 17461, 17469, 17777, 17793, 17803, 17847, 17887, 17913, 18039, 18279, 18299, 18417, 18475, 18543, 18653, 18657, 18925, 18927, 19047, 19067, 19629, 19791, 19953, 20937, 21897, 22793, 22975, 23679, 23787, 23949, 24489, 24597, 24775, 25299, 25569, 25699, 26379, 26757, 26919, 28489, 28739, 29984, 40201, 100051, 100095, 100185, 100365, 100545, 100569, 100633, 100635, 100691, 100816, 101066, 101318, 101392, 101445, 101593, 101715, 102271, 102326, 102345, 102435, 102615, 102832, 102961, 102963, 103065, 103089, 103139, 103245, 103593, 103605, 103869, 103937, 103971, 103975, 103977, 104057, 104097, 104143, 104235, 104349, 104415, 104505, 104679, 104727, 104787, 104853, 105136, 105313, 105405, 105483, 105489, 105593, 105597, 105712, 105759, 105775, 106035, 106039, 106239, 106569, 106617, 107117, 107247, 107249, 107373, 107407, 108091, 108105, 108121, 108122, 108189, 108341, 108475, 108507, 108567, 108729, 108925, 109117, 109137, 109377, 109399, 109539, 109801, 109957, 109971, 110131, 110138, 110177, 110265, 110535, 110997, 111013, 111165, 111169, 111184, 111255, 111472, 111707, 111783, 111902, 112154, 112155, 112287, 112319, 112333, 112335, 112537, 112605, 112624, 112779, 112801, 112912, 112975, 113055, 113235, 113237, 113414, 113415, 113459, 113503, 113543, 113547, 113673, 113697, 113859, 113873, 114045, 114064, 114177, 114287, 114315, 114429, 114461, 114775, 114979, 114993, 115035, 115059, 115215, 115273, 115305, 115504, 115529, 115563, 115941, 116067, 116115, 116357, 116575, 116771, 116823, 116829.

Some larger examples :