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congruent n.  and  triangular n.

First numbers that belong to both sets:

6, 15, 21, 28, 45, 55, 78, 120, 136, 190, 210, 231, 253, 276, 325, 351, 406, 465, 496, 561, 630, 703, 741, 820, 861, 903, 990, 1081, 1176, 1326, 1431, 1485, 1596, 1653, 1711, 1770, 1830, 2016, 2145, 2278, 2415, 2485, 2556, 2701, 2775, 2926, 3003, 3081, 3160, 3321, 3486, 3570, 3655, 3741, 3828, 4005, 4095, 4278, 4560, 4656, 4950, 5151, 5253, 5356, 5460, 5565, 5671, 5886, 6328, 6441, 6555, 6670, 6903, 7021, 7140, 7260, 7381, 7503, 7750, 8001, 8128, 8385, 8515, 8646, 8911, 9045, 9180, 9316, 9453, 9591, 9730, 9870, 10011, 10296, 10731, 10878, 11175, 11325, 11476, 11628, 11781, 11935, 12246, 12880, 13041, 13366, 13695, 13861, 14196, 14365, 14535, 14878, 15225, 15400, 15576, 15753, 16110, 16471, 16653, 17020, 17205, 17391, 17766, 17955, 18336, 18528, 19110, 19503, 19701, 19900, 20301, 20503, 20910, 21115, 21528, 21945, 22366, 22791, 23005, 23220, 23436, 23653, 23871, 24310, 24976, 25200, 25878, 26335, 26565, 27028, 27261, 27495, 27966, 28441, 28680, 28920, 29646, 30135, 30381, 30876, 31125, 31375, 31878, 32385, 32640, 32896, 33670, 34191, 34453, 34716, 35245, 35511, 36046, 36856, 37950, 38503, 38781, 39060, 39621, 39903, 40470, 41041, 41328, 41905, 42195, 42486, 43071, 43365, 43956, 44253, 44551, 44850, 45150, 46360, 46665, 47278, 47586, 47895, 48205, 48828, 49141, 49455, 50086, 51040, 52326, 52975, 53301, 53628, 54285, 54615, 55278, 56280, 56616, 57630, 58311, 58653, 58996, 59340, 59685, 60031, 60726, 61776, 62835, 63190, 63546, 63903, 64261, 64980, 65341, 65703, 66066, 66430, 67528, 67896, 68265, 69006, 69751, 70125, 70876, 71253, 71631, 72390, 73536, 73920, 75078, 75855, 76245, 76636, 77421, 77815, 78210, 78606, 79800, 81406, 82215, 82621, 83028, 83845, 84255, 85078, 86736, 87990, 88831, 89253, 90100, 90525, 90951, 91806, 93528, 93961, 94395, 94830, 95266, 95703, 96141, 97020, 97461, 97903, 98790, 99235.

Some larger examples :