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brilliant n.  and  equidigital n.

First numbers that belong to both sets:

10, 14, 15, 21, 25, 35, 49, 121, 169, 289, 361, 529, 841, 961, 1003, 1007, 1027, 1037, 1067, 1073, 1079, 1081, 1121, 1139, 1147, 1157, 1159, 1189, 1207, 1219, 1241, 1247, 1261, 1271, 1273, 1333, 1343, 1349, 1357, 1363, 1387, 1403, 1411, 1457, 1501, 1513, 1517, 1537, 1541, 1577, 1591, 1633, 1643, 1649, 1679, 1691, 1711, 1739, 1763, 1769, 1817, 1829, 1843, 1891, 1909, 1927, 1943, 1961, 2021, 2047, 2059, 2077, 2117, 2173, 2183, 2201, 2231, 2257, 2263, 2279, 2291, 2407, 2419, 2449, 2479, 2491, 2501, 2537, 2573, 2581, 2623, 2627, 2701, 2747, 2759, 2773, 2813, 2867, 2881, 2911, 2923, 2993, 3007, 3053, 3071, 3127, 3139, 3149, 3233, 3239, 3293, 3337, 3397, 3403, 3431, 3551, 3569, 3589, 3599, 3649, 3713, 3763, 3827, 3869, 3901, 3953, 3977, 4087, 4171, 4183, 4187, 4189, 4307, 4331, 4399, 4453, 4559, 4661, 4717, 4757, 4819, 4891, 4897, 5063, 5141, 5183, 5251, 5293, 5429, 5561, 5609, 5723, 5767, 5893, 5917, 5963, 6059, 6319, 6497, 6499, 6557, 6887, 7031, 7081, 7387, 7663, 8051, 8633, 100013, 100033, 100091, 100097, 100127, 100141, 100171, 100231, 100259, 100273, 100277, 100337, 100367, 100421, 100423, 100531, 100553, 100561, 100571, 100619, 100631, 100637, 100651, 100687, 100697, 100729, 100739, 100777, 100817, 100873, 100879, 100889, 100897, 100939, 100951, 100979, 101053, 101069, 101083, 101219, 101243, 101249, 101261, 101263, 101291, 101329, 101369, 101447, 101461, 101551, 101579, 101597, 101617, 101623, 101659, 101671, 101767, 101791, 101851, 101887, 101903, 101911, 101923, 101951, 101971, 102029, 102073, 102133, 102209, 102227, 102257, 102287, 102307, 102371, 102491, 102521, 102569, 102589, 102637, 102659, 102691, 102709, 102721, 102743, 102757, 102803, 102821, 102853, 102887, 102941, 102943, 102959, 102989, 102997, 103009, 103027, 103031, 103039, 103057, 103097, 103127, 103133, 103219, 103223, 103249, 103277, 103283, 103321, 103331, 103351, 103373, 103429.

Some larger examples :