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brilliant n.  and  lucky n.

First numbers that belong to both sets:

9, 15, 21, 25, 49, 169, 289, 319, 361, 391, 451, 517, 529, 559, 583, 781, 841, 961, 979, 1147, 1189, 1219, 1261, 1357, 1369, 1387, 1501, 1711, 2059, 2173, 2209, 2257, 2407, 2419, 2479, 2491, 2773, 2923, 3007, 3403, 3481, 3721, 3763, 4189, 4399, 4717, 4819, 5041, 5293, 5767, 5893, 7081, 7921, 9409, 10609, 11227, 14017, 14317, 15049, 15481, 16867, 17473, 17767, 17947, 18871, 19153, 19939, 20227, 22879, 22969, 22987, 22999, 23449, 23533, 23701, 24289, 24523, 24649, 25021, 25159, 25591, 26167, 26797, 27007, 27331, 27913, 28141, 28321, 28417, 28459, 28891, 29143, 29149, 29329, 29893, 30067, 30397, 30523, 30997, 31411, 32041, 32761, 33109, 33463, 33673, 34093, 34387, 34453, 34717, 35011, 35611, 35941, 36481, 36733, 37129, 37801, 37909, 38041, 38503, 38989, 39271, 39283, 39889, 40141, 40309, 40921, 40981, 41527, 41707, 41869, 41989, 42547, 42781, 42907, 43039, 43423, 43429, 43507, 43621, 43957, 44197, 44503, 44923, 44929, 45349, 46129, 46243, 46339, 47029, 47071, 47167, 47233, 47959, 48133, 48703, 49141, 49447, 49981, 50059, 50161, 50887, 51013, 51019, 51067, 51253, 51379, 51397, 51703, 51937, 52441, 52531, 52621, 52891, 52993, 53467, 53491, 53953, 54463, 54841, 54991, 55747, 56323, 56461, 56839, 57229, 57619, 57949, 58339, 58447, 58519, 58561, 58969, 59287, 59401, 59503, 59599, 59893, 60031, 60187, 60433, 60547, 60997, 61069, 61513, 62107, 62287, 62449, 62941, 64213, 64357, 64711, 64963, 66049, 66163, 66259, 66427, 66559, 66667, 67063, 67159, 67591, 67693, 68377, 68461, 68557, 68599, 68779, 69229, 69373, 69451, 69583, 69841, 69871, 70597, 71173, 71371, 71557, 71749, 71959, 71989, 72439, 72463, 73081, 73441, 73537, 73543, 73639, 74227, 74329, 75067, 75319, 75421, 75433, 75589, 75799, 75841, 76633, 76639, 77149, 77281, 77353, 78373, 78469, 78613, 78973, 79003, 79207, 79369, 79381, 79921, 79993, 80137, 80203, 80851, 81217, 81241, 81337, 81469, 81661, 81841.

Some larger examples :