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centered triangular n.  and  Ulam n.

First numbers that belong to both sets:

1, 4, 316, 409, 1489, 2584, 4294, 6049, 9721, 10459, 16069, 21064, 22510, 22879, 27541, 31756, 43096, 54436, 55585, 69016, 75601, 85324, 90406, 112204, 125716, 144616, 152164, 156010, 160885, 168841, 202585, 241804, 284491, 303076, 307135, 339151, 343444, 355024, 363835, 374251, 377254, 407944, 411079, 417385, 438211, 447994, 457885, 464539, 466210, 471241, 476299, 526585, 553585, 557236, 588754, 636679, 640594, 717259, 772210, 791704, 800446, 853906, 862984, 867541, 902101, 913771, 925516, 927874, 992674, 1019701, 1049599, 1072306, 1100389, 1128835, 1162921, 1224469, 1235335, 1243516, 1257211, 1474609, 1489519, 1498501, 1507510, 1516546, 1519564, 1528636, 1586719, 1617724, 1655326, 1760959, 1767466, 1856485, 1937449, 2065654, 2079760, 2147419, 2183464, 2260135, 2285986, 2364421, 2394649, 2413639, 2440351, 2591866, 2715556, 2796886, 2900236, 3060919, 3125539, 3314524, 3652741, 3699706, 3780235, 3794536, 3813646, 3861631, 3919609, 3963376, 3978019, 4031941, 4096135, 4155841, 4261366, 4266424, 4317169, 4342654, 4393849, 4419559, 4638484, 4659610, 4808836, 4835731, 4878919, 4944061, 4976794, 5075641, 5181034, 5259385, 5293144, 5400760, 5463559, 5509459, 5619241, 5735971, 5747710, 5847976, 5943136, 5955085, 6015010, 6117571, 6172219, 6196585, 6233224, 6251584, 6349960, 6356134, 6362311, 6387049, 6480244, 6706666, 6751144, 6783004, 6859774, 7001641, 7079635, 7112260, 7415929, 7543210, 7794181, 7828411, 7855849, 7869586, 7993759, 8701309, 8730235, 8824576, 8948710, 8970706, 9051589, 9147646, 9259111, 9468985, 9544510, 9605146, 9627934, 9696460, 9849610, 9872686, 9934354.