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gapful n.  and  triangular n.

First numbers that belong to both sets:

105, 120, 190, 231, 253, 300, 561, 990, 1035, 1275, 1485, 1540, 1770, 1830, 2080, 2775, 3003, 3240, 3570, 4005, 4095, 4186, 4560, 5050, 5151, 5995, 7140, 7875, 8256, 9180, 10153, 10440, 11175, 11325, 11628, 11781, 12090, 12720, 12880, 13530, 13695, 14535, 15225, 15400, 16110, 16290, 16653, 17020, 17205, 17391, 17955, 18336, 18915, 19110, 19701, 19900, 20100, 21736, 23220, 25200, 25425, 28680, 28920, 30135, 30628, 32640, 33930, 34980, 35245, 37950, 38781, 39060, 41041, 41328, 46360, 46665, 49455, 50403, 52650, 54285, 54615, 56616, 61425, 61776, 64620, 64980, 66066, 67161, 70125, 73920, 79800, 86320, 97020, 97461, 100576, 101025, 101475, 103740, 105570, 106030, 106491, 107880, 108345, 109278, 110685, 112101, 112575, 113050, 114960, 115440, 117370, 117855, 119805, 122265, 122760, 124750, 125250, 127260, 128271, 129795, 130305, 130816, 131328, 132870, 134940, 135460, 137550, 138075, 140715, 142845, 143380, 144991, 145530, 146070, 147696, 148240, 148785, 150975, 153735, 154290, 156520, 157080, 157641, 159330, 161028, 162165, 162735, 165600, 166176, 167910, 168490, 170820, 171405, 174345, 176121, 176715, 177310, 178503, 179700, 180300, 182710, 183315, 185136, 185745, 187578, 188805, 189420, 191890, 192510, 195000, 196251, 198135, 198765, 202566, 204480, 205120, 210925, 211575, 214840, 220116, 220780, 226128, 227475, 228826, 230181, 230860, 231540, 235641, 237016, 240471, 241860, 248160, 254541, 258840, 259560, 263175, 264628, 265356, 270480, 274911, 277140, 280875, 281625, 288420, 289180, 299925, 303810, 304590, 306936, 312445, 313236, 316410, 320400, 323610, 324415, 325221, 332520, 335790, 339900, 340725, 352380, 353220, 365085, 365940, 367653, 370230, 372816, 373680, 382375, 383250, 386760, 391170, 395605, 398278, 400960, 401856, 406351, 407253, 413595, 430128, 445096, 446040, 446985, 455535, 460320, 461280, 475800, 488566, 489555, 490545, 492528, 500500, 508536, 524800, 535095, 546535, 554931, 558096, 574056, 575128, 578350, 593505, 600060, 603351, 609960, 611065, 626640, 639015, 653796, 671061, 673380, 683865, 685035, 690900, 692076, 725410, 727821, 739936, 749700, 768180.

Some larger examples :