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centered nonagonal n.  and  triangular n.

First numbers that belong to both sets:

1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378, 1540, 1711, 1891, 2080, 2278, 2485, 2701, 2926, 3160, 3403, 3655, 3916, 4186, 4465, 4753, 5050, 5356, 5671, 5995, 6328, 6670, 7021, 7381, 7750, 8128, 8515, 8911, 9316, 9730, 10153, 10585, 11026, 11476, 11935, 12403, 12880, 13366, 13861, 14365, 14878, 15400, 15931, 16471, 17020, 17578, 18145, 18721, 19306, 19900, 20503, 21115, 21736, 22366, 23005, 23653, 24310, 24976, 25651, 26335, 27028, 27730, 28441, 29161, 29890, 30628, 31375, 32131, 32896, 33670, 34453, 35245, 36046, 36856, 37675, 38503, 39340, 40186, 41041, 41905, 42778, 43660, 44551, 45451, 46360, 47278, 48205, 49141, 50086, 51040, 52003, 52975, 53956, 54946, 55945, 56953, 57970, 58996, 60031, 61075, 62128, 63190, 64261, 65341, 66430, 67528, 68635, 69751, 70876, 72010, 73153, 74305, 75466, 76636, 77815, 79003, 80200, 81406, 82621, 83845, 85078, 86320, 87571, 88831, 90100, 91378, 92665, 93961, 95266, 96580, 97903, 99235, 100576, 101926, 103285, 104653, 106030, 107416, 108811, 110215, 111628, 113050, 114481, 115921, 117370, 118828, 120295, 121771, 123256, 124750, 126253, 127765, 129286, 130816, 132355, 133903, 135460, 137026, 138601, 140185, 141778, 143380, 144991, 146611, 148240, 149878, 151525, 153181, 154846, 156520, 158203, 159895, 161596, 163306, 165025, 166753, 168490, 170236, 171991, 173755, 175528, 177310, 179101, 180901, 182710, 184528, 186355, 188191, 190036, 191890, 193753, 195625, 197506, 199396, 201295, 203203, 205120, 207046, 208981, 210925, 212878, 214840, 216811, 218791, 220780, 222778, 224785, 226801, 228826, 230860, 232903, 234955, 237016, 239086, 241165, 243253, 245350, 247456, 249571, 251695, 253828, 255970, 258121, 260281, 262450, 264628, 266815, 269011, 271216, 273430, 275653, 277885, 280126, 282376, 284635, 286903, 289180, 291466, 293761, 296065, 298378, 300700, 303031, 305371, 307720, 310078, 312445, 314821, 317206, 319600, 322003, 324415, 326836, 329266, 331705, 334153, 336610, 339076, 341551, 344035, 346528, 349030, 351541.

Some larger examples :