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centered triangular n.  and  evil n.

First numbers that belong to both sets:

10, 46, 85, 136, 166, 235, 514, 571, 694, 760, 1396, 1489, 1786, 2110, 2224, 2584, 2710, 2971, 3106, 3244, 3826, 3979, 5491, 5674, 6634, 6835, 7669, 8104, 8326, 8779, 9010, 9964, 10210, 10459, 10966, 11224, 12016, 12286, 12835, 13114, 13396, 13681, 14554, 14851, 15151, 18985, 20011, 22879, 24004, 24385, 25546, 25939, 26734, 27136, 28360, 29611, 30034, 30889, 33526, 33976, 35344, 35806, 36271, 36739, 38161, 40099, 40591, 41086, 41584, 43096, 43606, 44635, 45154, 45676, 46729, 47260, 48331, 48871, 49960, 50509, 51061, 51616, 52174, 53866, 56746, 57919, 58510, 59104, 60301, 60904, 62119, 65209, 66466, 69661, 70960, 75601, 76954, 79696, 83191, 84610, 85324, 86041, 87484, 89671, 92629, 94126, 95635, 96394, 100234, 101011, 102574, 104149, 106534, 108139, 108946, 109756, 110569, 113026, 113851, 118021, 118864, 123985, 126586, 128335, 129214, 132760, 133654, 136354, 137260, 138169, 139996, 140914, 142759, 144616, 145549, 147424, 148366, 150259, 156010, 157951, 158926, 159904, 160885, 162856, 163846, 164839, 165835, 167836, 168841, 170860, 171874, 172891, 174934, 175960, 179056, 180094, 181135, 182179, 188506, 189571, 191710, 193861, 196024, 199291, 200386, 202585, 203689, 211501, 217171, 219460, 220609, 224074, 226399, 227566, 231085, 232264, 233446, 235819, 238204, 239401, 240601, 241804, 244219, 245431, 247864, 250309, 253999, 256474, 257716, 261460, 262714, 267760, 270301, 276706, 281884, 284491, 285799, 288424, 291061, 300385, 301729, 304426, 305779, 307135, 309856, 312589, 313960, 316711, 318091, 320860, 322249, 326434, 329239, 332056, 333469, 334885, 343444, 344881, 346321, 347764, 349210, 350659, 352111, 353566, 356485, 357949, 362359, 371260, 380269, 383296, 386335, 390916, 392449, 397066, 398611, 401710, 404821, 407944, 409510, 411079, 412651, 420556, 425335, 426934, 428536, 434974, 436591, 438211, 439834, 451279, 452926, 454576, 462871, 467884, 469561, 472924, 479686, 483085, 484789, 493354, 500260, 503731, 512461, 514216, 524809, 526585, 528364, 530146, 535510, 537304, 544510, 549946, 557236, 559066, 560899, 562735, 566416, 568261, 570109, 575671.

Some larger examples :