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equidigital n.  and  tau n.

First numbers that belong to both sets:

1, 2, 384, 448, 640, 896, 1152, 1344, 1408, 1664, 1920, 1944, 2000, 2025, 2176, 2240, 2432, 2688, 2944, 3456, 3712, 3968, 4480, 4736, 5000, 5248, 5504, 5625, 6016, 6144, 6784, 6912, 7552, 7680, 7776, 7808, 8576, 9088, 9344, 10304, 10880, 11136, 11250, 11264, 11648, 11904, 12000, 12096, 12160, 12321, 12928, 12960, 12992, 13184, 13440, 13696, 13888, 13952, 14000, 14208, 14464, 14720, 15000, 15129, 15232, 15744, 16256, 16512, 16576, 16641, 16768, 17024, 17280, 17536, 17792, 18048, 18368, 18432, 18560, 18816, 19072, 19264, 19328, 19440, 19840, 19881, 20096, 20352, 20412, 20608, 20864, 21056, 21376, 22144, 22656, 22912, 23040, 23168, 23424, 23680, 23744, 24192, 24448, 24704, 25216, 25281, 25472, 25728, 25984, 26240, 26432, 27008, 27264, 27328, 27440, 27520, 27776, 28032, 28160, 28544, 29056, 29312, 29824, 30000, 30016, 30080, 30336, 30592, 30720, 30848, 31329, 31808, 31872, 32128, 32704, 32896, 32928, 33152, 33280, 33489, 33664, 33920, 34176, 34432, 34560, 34688, 35000, 35392, 35456, 35968, 36224, 36736, 37184, 37248, 37504, 37760, 38400, 38528, 38880, 39040, 39296, 39808, 39872, 40064, 40401, 40576, 40824, 42112, 42368, 42880, 43008, 43136, 43456, 43520, 44416, 44672, 45184, 45369, 45440, 45952, 46720, 46976, 47488, 47744, 47961, 48000, 48384, 48512, 48640, 49024, 49792, 50560, 50816, 51328, 51840, 52352, 52864, 53120, 53248, 53632, 53760, 53888, 54432, 54656, 55168, 55296, 55424, 56000, 56169, 56192, 56704, 56960, 57472, 58496, 58880, 59008, 59264, 59776, 60000, 60032, 61312, 62001, 62080, 62336, 62848, 63616, 63872, 64384, 65152, 65408, 65856, 66688, 66944, 69120, 69248, 70000, 70016, 70784, 71289, 71296, 71442, 72064, 72832, 73088, 73856, 74240, 74368, 75136, 75904, 76672, 76928, 77696, 78464, 78976, 79232, 79360, 79744, 80768, 82048, 82304, 82816, 83584, 84352, 84608, 84681, 86144, 86656, 86912, 87424, 88448, 89728, 90752, 92032, 93056, 93824, 94592, 94720, 95104, 96040, 96128.

Some larger examples :