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arithmetic n.  and  triangular n.

First numbers that belong to both sets:

1, 3, 6, 15, 21, 45, 55, 66, 78, 91, 105, 153, 190, 210, 231, 253, 276, 351, 378, 406, 435, 465, 561, 595, 630, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1275, 1326, 1431, 1485, 1540, 1653, 1711, 1770, 1830, 1891, 2016, 2145, 2211, 2278, 2346, 2415, 2485, 2556, 2701, 2850, 2926, 3003, 3081, 3160, 3403, 3486, 3570, 3655, 3741, 3828, 3916, 4005, 4095, 4186, 4278, 4371, 4465, 4560, 4753, 4851, 4950, 5151, 5253, 5460, 5565, 5671, 5778, 5886, 5995, 6105, 6216, 6328, 6441, 6555, 6670, 6903, 7021, 7140, 7503, 7626, 7750, 7875, 8385, 8515, 8646, 8778, 8911, 9045, 9180, 9316, 9453, 9591, 9730, 9870, 10011, 10153, 10585, 10731, 10878, 11175, 11628, 11781, 11935, 12090, 12246, 12403, 12561, 13366, 13530, 13695, 13861, 14028, 14365, 14535, 14706, 14878, 15051, 15225, 15400, 15576, 15753, 15931, 16110, 16471, 16653, 16836, 17020, 17205, 17391, 17578, 17766, 17955, 18145, 18336, 18528, 18721, 18915, 19110, 19503, 19701, 20301, 20503, 20706, 20910, 21115, 21321, 21528, 21736, 21945, 22155, 22366, 22578, 22791, 23005, 23220, 23653, 23871, 24090, 24310, 24531, 24753, 25651, 25878, 26106, 26335, 26565, 26796, 27028, 27261, 27495, 27730, 27966, 28203, 28441, 28680, 29646, 30135, 30381, 30876, 31125, 31375, 31626, 31878, 32131, 32385, 33153, 33411, 33670, 34191, 34453, 34716, 34980, 35245, 35511, 35778, 36046, 36315, 36585, 36856, 37128, 37401, 37675, 37950, 38226, 38503, 39340, 39621, 39903, 40186, 40470, 40755, 41041, 41905, 42195, 42486, 43071, 43365, 43660, 43956, 44253, 44551, 44850, 45150, 45451, 45753, 46056, 46665, 46971, 47278, 47586, 47895, 48205, 48516, 49141, 49455, 49770, 50086, 50403, 50721, 51040, 51360, 51681, 52003, 52326, 53301, 53628, 53956, 54285, 54615, 54946, 55278, 55611, 55945, 56280, 56616, 56953, 57291, 57630, 57970, 58311, 59340, 59685, 60031, 60378.

Some larger examples :