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brilliant n.  and  self n.

First numbers that belong to both sets:

9, 121, 143, 187, 209, 299, 323, 703, 793, 817, 1357, 1513, 1537, 1649, 1739, 1829, 2077, 2257, 2279, 2773, 3337, 3403, 3763, 4819, 5293, 5429, 6059, 6889, 9409, 11413, 11639, 13843, 14317, 15553, 16789, 17869, 18769, 19153, 19511, 19781, 19939, 20099, 20413, 20437, 20819, 21583, 22663, 22999, 24823, 25273, 26219, 27029, 27499, 29143, 29321, 29591, 29929, 30067, 30179, 30629, 31439, 31753, 32743, 32899, 33127, 33463, 33823, 34093, 34117, 34453, 35263, 35621, 37399, 37669, 38771, 39289, 39917, 40259, 40349, 40619, 41989, 42037, 42059, 42127, 42149, 42733, 42799, 43139, 43229, 43273, 43363, 43811, 44173, 44599, 45499, 46243, 46961, 47053, 47233, 48043, 48133, 48199, 48379, 48827, 48941, 49729, 50137, 50249, 50429, 52001, 52093, 52319, 52699, 53083, 53869, 54253, 55421, 55669, 55961, 56323, 56839, 57311, 57469, 57671, 58033, 58301, 59291, 59987, 60799, 61093, 61811, 63433, 63523, 63881, 64219, 65411, 65591, 66043, 66289, 66559, 66581, 66761, 67841, 68269, 68359, 68987, 69169, 69527, 69551, 69731, 70723, 71173, 71219, 71779, 71959, 72433, 73153, 74299, 74951, 75043, 75199, 75311, 75469, 75827, 75851, 76033, 76121, 76459, 76639, 76729, 77089, 77179, 77381, 77629, 78371, 78731, 79091, 79517, 79921, 80419, 81253, 81859, 82063, 82333, 83411, 83569, 83659, 84043, 84109, 84671, 84739, 85279, 85301, 85907, 86741, 86897, 87349, 87707, 88091, 88181, 88271, 88631, 88831, 89081, 89239, 89351, 89933, 90119, 90319, 90521, 90589, 90791, 90949, 91489, 91601, 92501, 92749, 92839, 93017, 93469, 93829, 94189, 94301, 94481, 95807, 96641, 97271, 97541, 97697, 97921, 98171, 99677, 99811, 100739, 100873, 101369, 101617, 102853, 102943, 103009, 103057, 104653, 104809, 104921, 105011, 105283, 105419, 105463, 105799, 105979, 106027, 106049, 107533, 107623, 107689, 107869, 108611, 108679, 109309, 109601, 109691, 110189, 110213, 110549, 110683, 110953, 111313, 111583, 112169, 112439, 112529, 113249, 113293, 114823, 114911, 115519, 115543, 116353, 116509, 116621.

Some larger examples :