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brilliant n.  and  repunit

First numbers that belong to both sets:

15, 21, 121, 341, 703, 781, 871, 1261, 1333, 2047, 2257, 33673, 50851, 54991, 63757, 71557, 79243, 89701, 102721, 104653, 107257, 131407, 132133, 137561, 147841, 166057, 169333, 191407, 194923, 212983, 213907, 216691, 297571, 345157, 460363, 463081, 1335181, 1807681, 1978243, 2701093, 2740681, 2763907, 2803951, 2967007, 2984257, 3259831, 3513751, 3676807, 3746161, 3753907, 4193821, 4270423, 4382743, 4522003, 4793911, 4877473, 5064751, 5114383, 5209807, 5463907, 5529553, 5791243, 6098431, 6413557, 6700333, 6998671, 7587271, 7882057, 7887673, 8040061, 8430313, 8552701, 8570257, 8859553, 9378907, 9477163, 9489481, 9563557, 9582121, 9737521, 9750007, 10014061, 10096507, 10345873, 10436131, 10617823, 10676557, 10689631, 11045653, 11065603, 11125561, 11373757, 11631511, 11672473, 11740903, 11885257, 12030493, 12155683, 12934813, 13202323, 13553443, 13686301, 13909171, 14133841, 14194057, 14421007, 14565673, 15190507, 15448831, 15820507, 15876241, 16261057, 16325641, 16715833, 16822303, 17593831, 17762011, 17871757, 18297007, 18305563, 18761893, 20191543, 20272507, 20625223, 22369621, 22805401, 22872307, 23275801, 23537053, 24024703, 24925057, 25065043, 25760701, 25892833, 26096773, 26837581, 26962057, 27873121, 27968233, 27999973, 28074103, 28392913, 28542307, 29360143, 30808051, 31635001, 32211301, 32484301, 32941861, 34615573, 35325193, 35994001, 37021141, 37411573, 38198581, 38856523, 39419563, 39608143, 40761841, 40979203, 41841493, 44402233, 44682541, 45636781, 45771991, 47616901, 48951013, 49287421, 50161807, 51876007, 54015151, 56422633, 57206533, 58209271, 60925831, 64120057, 64152091, 64360507, 65618101, 66528493, 78419881, 82455481, 125294443, 141075007, 141764743, 143292871, 143484463, 151819363, 151942603, 164083291, 164955493, 165624031, 181346623, 188966263, 190923307, 194783893, 201938311, 205735993, 214344241, 218551873, 222412483, 222740701, 226246723, 228720253, 231359311, 231998593, 235177561, 235484371, 239336371, 242689663, 243718933, 249877057, 251492023, 258100291, 258582481, 260289823, 262942441, 267502381, 268517383, 270849307, 271244431, 276207781, 276839683, 279140557, 280813807, 282929221, 284242741, 285998833, 287896057, 292392901, 300346231, 302464273, 312776911, 314016121, 314583433, 314902771, 317249533, 323442241, 323694073, 324450157, 324954703, 330967057, 331622311, 347095531, 347430961, 350644351, 353797291, 355492171, 355643023, 358023163, 359462641, 365670007, 366014293, 367853221, 368390443, 368659201, 372586507, 373281721, 373513603, 374209681, 375448753, 387400807, 388700941, 391901413, 395711557, 396547483, 396906007, 397184971, 400180021, 404030101, 416792641, 417732283, 417854923, 419573773, 420721633, 423186613, 424257007, 426154093, 428096791, 430500253.

Some larger examples :