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centered triangular n.  and  sphenic n.

First numbers that belong to both sets:

1054, 1786, 2110, 2710, 4294, 5134, 6634, 7885, 8326, 10210, 12835, 13114, 14554, 17014, 22510, 24769, 25546, 26335, 30889, 32635, 36271, 42085, 44635, 45154, 47794, 49414, 52174, 52735, 53866, 56746, 58510, 61510, 63346, 66466, 68374, 71614, 73594, 75601, 76954, 84610, 88210, 88939, 90406, 94126, 95635, 100234, 113026, 115510, 117181, 119710, 122266, 123985, 126586, 133654, 136354, 141835, 148366, 150259, 151210, 156010, 158926, 160885, 165835, 171874, 174934, 180094, 181135, 199291, 202585, 209254, 214894, 218314, 220609, 224074, 225235, 231085, 233446, 234631, 249085, 252766, 266494, 272854, 274135, 276706, 280585, 283186, 287110, 316711, 326434, 327835, 329239, 330646, 353566, 356485, 357949, 360886, 377254, 389386, 392449, 411079, 425335, 431749, 434974, 447994, 449635, 456229, 483085, 493354, 501994, 512461, 517735, 521266, 530146, 535510, 548131, 553585, 559066, 560899, 562735, 568261, 573814, 579394, 583129, 585001, 588754, 594406, 609610, 644521, 666334, 668335, 672346, 682426, 704866, 719335, 721414, 727669, 731854, 750835, 752959, 783010, 800446, 807034, 818074, 820291, 824734, 849385, 853906, 872110, 876691, 883585, 895135, 902101, 927874, 930235, 939709, 946846, 954010, 966010, 973246, 978085, 980509, 1004914, 1007371, 1017229, 1024654, 1044586, 1052110, 1059661, 1072306, 1077385, 1085026, 1090135, 1092694, 1113274, 1118449, 1134046, 1147126, 1152379, 1160281, 1162921, 1189486, 1192159, 1197514, 1205569, 1238059, 1254466, 1262710, 1298746, 1304335, 1307134, 1321174, 1329634, 1343794, 1352326, 1360885, 1445014, 1450909, 1459774, 1462735, 1468666, 1483546, 1492510, 1510519, 1534699, 1556014, 1565194, 1614610, 1630210, 1639606, 1649029, 1655326, 1661635, 1664794, 1680634, 1690174, 1696549, 1706134, 1712539, 1725385, 1731826, 1747981, 1751221, 1773985, 1790335, 1793614, 1839835, 1856485, 1863166, 1866511, 1883281, 1900126, 1923835, 1927234, 1937449, 1954534, 1971694, 1982026, 1988929, 2002771, 2009710, 2037586, 2055106, 2062135, 2065654, 2083294, 2093914, 2111674, 2115235, 2122366, 2133085, 2158201, 2169010, 2179846, 2187085, 2197966, 2230771, 2267506, 2274889, 2289691, 2297110, 2315710, 2319439, 2326906, 2364421, 2409835, 2417446, 2444179, 2474911, 2478766, 2505835, 2509714, 2521369, 2533051, 2536951, 2540854, 2548669, 2564335, 2583985, 2591866, 2623510.

Some larger examples :