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brilliant n.  and  octagonal n.

First numbers that belong to both sets:

21, 341, 481, 1541, 31621, 38081, 48133, 56033, 79381, 83333, 97921, 109061, 111361, 133141, 188501, 197633, 206981, 219781, 229633, 256961, 282133, 293281, 328021, 3076481, 3125281, 3375041, 3387781, 3542533, 3568661, 3647621, 3985921, 4111381, 4181921, 4224533, 4411681, 4543621, 4588033, 4935701, 5044033, 5090821, 5122133, 5603333, 6157601, 6278533, 6330721, 6577121, 6594901, 6955541, 7028821, 7232321, 7648033, 7686401, 7879681, 8036033, 8233633, 8293381, 8333333, 8595361, 8902741, 9006401, 9533701, 9835541, 10386241, 10837601, 10974881, 11182421, 11415301, 12032021, 12322133, 13012501, 13390081, 13747361, 13773061, 14005441, 14555221, 14608133, 14687681, 14794081, 15008033, 15604321, 16324001, 16520533, 16661633, 16945633, 17174561, 17812033, 17870561, 18342241, 18790021, 19061281, 19212821, 19609633, 21397381, 21654533, 22369621, 22533761, 23129633, 23464033, 24242261, 24550241, 25172033, 25276421, 25696133, 26332181, 27012001, 27409541, 27664033, 28103041, 28213333, 31040833, 31118081, 31817633, 32091781, 32683201, 33120341, 302204033, 303651041, 305464661, 306191621, 310693633, 311671361, 312773141, 314736661, 315351521, 316583041, 319053281, 321781633, 327774721, 328402181, 334963333, 339033221, 342614533, 346859521, 348668321, 351910021, 355297301, 356604421, 360145633, 361198241, 367678981, 368476501, 370740833, 371675221, 374753633, 376096033, 377171681, 379732501, 380137633, 383793541, 384472481, 386649121, 388695301, 390609941, 391431941, 392803861, 396106261, 400253701, 402752533, 404840833, 405956801, 411840833, 413670661, 417767201, 418192133, 418617281, 419184481, 419894021, 427165601, 429890581, 434644033, 437247841, 439714133, 443353633, 446715221, 449501761, 451118981, 453919201, 457320533, 459248641, 460585861, 461329601, 464012033, 465505633, 468500033, 468950021, 470000833, 470752133, 472708321, 474970501, 477086741, 480269921, 481637381, 488656981, 490803461, 493108481, 495573121, 498662561, 500520833, 500985941, 502382561, 504870241, 507520133, 509551201, 518504533, 518820101, 520399381, 528013333, 531681281, 532800133, 533600033, 536003333, 538412033, 539537941, 542761301, 543730181, 544861633, 545670533, 549724033, 552163333, 554118661, 557058133, 557548801, 562467361, 563947141, 564770081, 567737633, 569720321, 573862021, 574692161, 577352641, 578185301, 580186133, 580686881, 581354881, 584868181, 592769633, 600893921, 604636033, 608560661, 609244501, 611812321, 615244481, 615416341, 615760133, 620928533, 622137601, 624732421, 633595201, 633944033, 634467461, 635165701, 635689633, 638837761, 644453633, 651861761, 652923521, 656824033, 659846021, 670208533, 670567301, 680471041, 682460501, 684634133, 685903681, 689537441, 696102401, 709879301, 710617861, 712650881, 713946133, 715427861, 716169301, 717096641, 717653333, 720068161, 720440033, 728458501, 730704133, 746331041, 748604033.

Some larger examples :