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brilliant n.  and  star n.

First numbers that belong to both sets:

121, 253, 793, 1261, 1633, 2773, 3901, 11881, 19153, 24961, 49141, 50233, 59401, 90037, 128773, 162361, 186913, 197653, 268393, 294373, 422941, 492493, 1425937, 1515037, 1663213, 1811701, 2092141, 2185273, 2601733, 3020341, 3063061, 3175537, 3254593, 3272293, 3343573, 3970693, 4029481, 4289221, 4329901, 4381021, 4442761, 4662253, 4747261, 5083921, 5307241, 5397913, 5466421, 5489353, 5558437, 5604733, 5862793, 6006001, 6054121, 6322213, 6824533, 6991921, 7213873, 7439293, 7886773, 8108437, 9055273, 9143941, 9639337, 9792037, 9930493, 10194673, 10478173, 10637353, 10765561, 11008021, 11171161, 11335501, 11385037, 11751601, 11886337, 11953993, 12038833, 12623701, 13080313, 13653433, 13798633, 13981213, 14424301, 14648437, 14855413, 15912073, 16226281, 16964653, 17411473, 17678233, 17781373, 17843401, 18385501, 18935713, 19732693, 19754461, 19798033, 20501713, 21900061, 21968893, 22360981, 23061361, 23748661, 23796433, 25945921, 26271337, 27954733, 28501321, 29370937, 29770537, 29877553, 31204081, 31258837, 31341061, 32252653, 32615353, 33346837, 33829501, 33972121, 34172293, 34603213, 35240113, 37155793, 37455013, 38481337, 38846881, 39367693, 39830113, 40482037, 41865133, 43529653, 45127837, 48991837, 49335337, 49438621, 50547037, 54450937, 56715301, 57790273, 59289553, 80176081, 84262537, 92363113, 140698837, 141805093, 159536953, 171638713, 181467001, 193404037, 199930537, 201248833, 202571461, 208966213, 209887861, 211452193, 214024537, 223662781, 227045713, 230082337, 232391713, 233288761, 234637573, 235088041, 240071701, 248725693, 249266821, 250971337, 253851121, 260370937, 261241213, 262112941, 267373801, 268335937, 273577537, 281658313, 282892933, 283552501, 285867037, 288440533, 290774893, 301736233, 310824037, 316463437, 317073781, 318471061, 320572741, 321011461, 322945393, 324002713, 326565037, 326742121, 327185041, 328071781, 334581337, 339889213, 340612141, 342785533, 359306293, 364057861, 373181293, 374412601, 381364537, 384048001, 388476973, 401130913, 404966641, 407533933, 413290201, 421799041, 422402941, 422604337, 424822861, 427047193, 428465701, 431309773, 434571661, 436104901, 438153421, 439487533, 439590241, 441441037, 442780141, 446395501, 446809621, 450753337, 452002321, 455550493, 456492037, 458482933, 464059381, 466595653, 467019037, 469669537, 472008181, 474886273, 475420213, 476488993, 485622073, 487242793, 488000053, 492338533, 495386893, 496150453, 497133037, 500086621, 502609537, 503928361, 507343321, 508336921, 510769813, 523245493, 527850121, 527962681, 529201633, 530329213, 534851533, 535985113, 536325421, 536665837, 538142221, 538255873, 542355337, 543040093, 546012361, 546813973, 566462233, 572424337, 574653493, 577475461, 581721373, 587881813, 588713581, 593477821, 601500937, 603184213, 607523437, 609094201, 609819853, 614911513, 618439537.

Some larger examples :