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centered triangular n.  and  pernicious n.

First numbers that belong to both sets:

10, 19, 31, 109, 136, 199, 274, 316, 361, 409, 460, 514, 631, 829, 901, 976, 1054, 1135, 1219, 1306, 1585, 1684, 1891, 2341, 2461, 2839, 3385, 3529, 3676, 4135, 4294, 4456, 4621, 4789, 4960, 5134, 5860, 6049, 6241, 6436, 7039, 7246, 7456, 8551, 9244, 9481, 12559, 13969, 15760, 16381, 16696, 17014, 17986, 18316, 18649, 19666, 20710, 21064, 21781, 22144, 22510, 23626, 24769, 25156, 26335, 28774, 29191, 30460, 31756, 32635, 33079, 34885, 37210, 37684, 39124, 42085, 49414, 52735, 53299, 54436, 55585, 57331, 61510, 63346, 63964, 65836, 67099, 67735, 68374, 69016, 70309, 71614, 73594, 74260, 74929, 78319, 80389, 81085, 81784, 82486, 83899, 88210, 88939, 90406, 91144, 91885, 93376, 94879, 98689, 99460, 101791, 103360, 104941, 105736, 117181, 119710, 120559, 122266, 124849, 127459, 130981, 131869, 135451, 141835, 143686, 149311, 152164, 153121, 169849, 173911, 176989, 178021, 183226, 184276, 185329, 186385, 190639, 192784, 194941, 201484, 204796, 205906, 212629, 213760, 214894, 216031, 221761, 225235, 229909, 237010, 246646, 249085, 252766, 258961, 260209, 263971, 265231, 271576, 274135, 275419, 277996, 280585, 283186, 287110, 289741, 292384, 293710, 299044, 303076, 311221, 315334, 319474, 325036, 327835, 336304, 337726, 339151, 342010, 359416, 363835, 365314, 368281, 372754, 374251, 375751, 381781, 384814, 387859, 393985, 395524, 400159, 403264, 406381, 414226, 417385, 422146, 423739, 441460, 446356, 447994, 449635, 456229, 457885, 459544, 464539, 474610, 477991, 488206, 495076, 498529, 501994, 507214, 508960, 510709, 515974, 517735, 519499, 521266, 523036, 531931, 539101, 540901, 564574, 583129, 586876, 596296, 600085, 605791, 621139, 623071, 626944, 636679, 638635, 642556, 644521, 652411, 654391, 660349, 666334, 668335, 676369, 678385, 682426, 694621, 700759, 708985, 715186, 723496, 727669, 729760, 731854, 742369, 748714, 750835, 759349, 763624, 774364, 776521, 780844, 783010, 789526, 791704, 802639, 804835, 815860, 820291, 824734, 838135, 847129, 849385, 865261, 883585, 885889, 892819, 904429, 909094, 911431, 913771, 925516, 927874.

Some larger examples :