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brilliant n.  and  triangular n.

First numbers that belong to both sets:

6, 10, 15, 21, 253, 703, 1081, 1711, 1891, 2701, 3403, 25651, 34453, 38503, 49141, 60031, 64261, 73153, 79003, 88831, 104653, 108811, 114481, 126253, 146611, 158203, 171991, 188191, 218791, 226801, 258121, 269011, 286903, 351541, 371953, 385003, 392941, 482653, 497503, 2035153, 2053351, 2077741, 2126953, 2201851, 2284453, 2434321, 2741311, 2992681, 3022111, 3059101, 3270403, 3324331, 3363121, 3913003, 3971971, 4082653, 4142881, 4212253, 4255903, 4388203, 4495501, 4567753, 4686391, 4862521, 5013361, 5128003, 5176153, 5292631, 5489641, 6008311, 6186403, 6561253, 6969511, 7138531, 7229503, 7459453, 7787431, 8026021, 8086231, 8231653, 8317081, 8514001, 8563591, 8725753, 9067411, 9080191, 9131401, 9169903, 9493903, 9863461, 10335331, 10403641, 10679131, 10944181, 11056753, 11455291, 11512801, 12095821, 12169711, 12890503, 12936241, 12997351, 13012651, 13073941, 13694761, 14507191, 14571901, 14652991, 14783203, 15028903, 15160771, 15576571, 15896341, 16253551, 16857721, 17278381, 17561701, 17632891, 18225703, 18280081, 18443701, 18736381, 18809911, 19328653, 20081953, 20234341, 20310751, 21770101, 22028203, 22167811, 22187791, 22569121, 22974031, 22994371, 23300551, 23794651, 24377653, 24482503, 24904153, 25052581, 25822891, 26017291, 26255881, 27331921, 27509653, 27956503, 28294003, 28406953, 28565461, 28929421, 29203903, 29664253, 29849401, 30058381, 30595753, 31470211, 32308741, 32429431, 32817151, 33182731, 33796531, 34590403, 34890481, 35469253, 35798491, 36307981, 36487153, 37649503, 37831951, 37962541, 38250631, 38566153, 38882971, 39547171, 40163203, 40621591, 41710411, 42149971, 42702661, 43036003, 44807311, 45950491, 46094401, 46672291, 47253781, 47458153, 48191653, 48398041, 48871441, 49019851, 49735351, 202457503, 203666653, 206583301, 207132481, 210258271, 210812311, 210997153, 212726251, 213035761, 213469453, 217517653, 220531501, 221730211, 221793391, 224264431, 224582221, 225282151, 226366003, 227132641, 228605653, 229376071, 230405311, 232470703, 232794253, 233247601, 234610291, 234870301, 236890261, 238001653, 244061371, 249593653, 253158751, 254781451, 255866131, 256341403, 258519691, 259612291, 263179153, 264350521, 265386241, 265731931, 266770351, 268158061, 268505551, 273744901, 277477903, 277689961, 278539003, 279105751, 279956953, 280312003, 282589651, 283660471, 285091381, 286023403, 288540253, 289983403, 290344753, 292880503, 293752441, 297838621, 298204831, 299671921, 300774601, 304020811, 307061371, 308550061, 313338061, 316349281, 318465703, 320209471, 321121153, 326695141, 327232153, 328768903, 329153653, 332781301, 334020781, 335884321, 336273211, 338065003, 338455153, 340565851, 345674071, 346305403, 349470703, 350026111, 351058753, 354485251.

Some larger examples :