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congruent n.  and  pronic n.

First numbers that belong to both sets:

6, 20, 30, 56, 110, 156, 182, 210, 240, 306, 342, 380, 462, 552, 600, 702, 756, 870, 992, 1122, 1190, 1332, 1406, 1482, 1560, 1640, 1806, 1980, 2070, 2256, 2550, 2652, 2756, 2862, 2970, 3192, 3422, 3540, 3660, 3782, 3906, 4032, 4160, 4290, 4422, 4692, 4830, 5112, 5550, 5852, 6006, 6320, 6480, 6806, 6972, 7140, 7310, 7832, 8010, 8190, 8372, 8556, 8742, 9312, 9506, 9702, 10100, 10302, 10712, 10920, 11342, 11772, 11990, 12432, 12656, 13110, 13340, 13806, 14280, 14520, 15006, 15252, 15750, 16256, 17030, 17556, 17822, 18360, 19182, 19740, 20022, 20306, 20592, 20880, 21170, 21462, 21756, 22350, 22952, 23256, 23870, 24180, 24806, 25122, 25440, 25760, 26406, 26732, 27060, 27390, 28056, 29070, 29756, 30102, 30800, 31862, 32220, 32580, 32942, 33306, 34040, 34782, 35156, 35532, 35910, 36672, 37830, 38612, 39006, 39800, 41006, 41820, 42230, 43056, 43472, 43890, 44310, 44732, 45582, 46872, 47742, 48180, 48620, 49062, 49952, 50400, 50850, 51302, 52212, 52670, 53592, 54522, 54990, 55932, 56406, 57840, 58806, 59292, 60270, 61752, 62750, 63252, 64262, 64770, 65280, 65792, 66306, 66822, 67340, 67860, 68382, 69432, 69960, 71022, 72092, 72630, 73712, 74256, 74802, 75350, 75900, 77006, 78120, 78680, 79806, 80372, 80940, 81510, 82656, 84390, 85556, 86142, 86730, 87320, 89102, 90300, 90902, 92112, 93330, 93942, 94556, 95790, 97656, 98910, 99540, 100806, 102080, 102720, 103362, 104006, 104652, 105300, 105950, 107256, 108570, 109230, 110556, 111222, 113232, 113906, 114582, 115260, 116622, 117992, 118680, 120062, 120756, 122150, 122850, 124256, 124962, 125670, 126380, 127092, 127806, 129240, 131406, 132860, 133590, 135792, 136530, 137270, 138012, 138756, 139502, 140250, 141752, 142506, 143262, 144020, 145542, 147072, 147840, 148610, 149382, 150932, 151710, 153272, 155630, 157212, 158006, 158802, 159600, 161202, 162006, 162812, 163620, 164430, 166872, 168510, 169332, 170982, 172640, 175142, 176820, 177662, 179352, 181902, 183612, 184470.

Some larger examples :