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arithmetic n.  and  centered triangular n.

First numbers that belong to both sets:

1, 19, 31, 46, 85, 109, 166, 199, 235, 361, 409, 460, 571, 631, 694, 829, 901, 1054, 1135, 1219, 1489, 1585, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2710, 2839, 2971, 3385, 3529, 3979, 4135, 4294, 4621, 4789, 4960, 5134, 5311, 5860, 6049, 6241, 6634, 6835, 7039, 7246, 7669, 7885, 8326, 8551, 8779, 9481, 9721, 9964, 10459, 10711, 10966, 11224, 11485, 11749, 12286, 12559, 12835, 13114, 13396, 13681, 13969, 14260, 14554, 14851, 15151, 15454, 16069, 16381, 16696, 17014, 17335, 17659, 18649, 18985, 20011, 20359, 20710, 21421, 21781, 22510, 22879, 23251, 24004, 24385, 24769, 25939, 26335, 26734, 27541, 27949, 28774, 29191, 29611, 30460, 30889, 31321, 31756, 32635, 33079, 33526, 33976, 34429, 34885, 35806, 36271, 36739, 38161, 38641, 40099, 40591, 41086, 42085, 42589, 43606, 44119, 44635, 45154, 46201, 46729, 47260, 47794, 48331, 48871, 49414, 50509, 51061, 52174, 52735, 53299, 53866, 55009, 55585, 57331, 57919, 58510, 59104, 59701, 60301, 60904, 61510, 62119, 62731, 63346, 64585, 65209, 66466, 67099, 67735, 68374, 69661, 70309, 71614, 72271, 72931, 73594, 74260, 74929, 75601, 77635, 79006, 80389, 81085, 81784, 82486, 83191, 83899, 85324, 86041, 86761, 88939, 89671, 90406, 91885, 92629, 94126, 94879, 95635, 97156, 97921, 98689, 99460, 100234, 101011, 101791, 102574, 104149, 104941, 106534, 107335, 108139, 108946, 109756, 110569, 111385, 113026, 113851, 114679, 115510, 116344, 117181, 118021, 118864, 119710, 120559, 121411, 123985, 124849, 125716, 126586, 127459, 128335, 129214, 130981, 131869, 132760, 133654, 134551, 135451, 136354, 137260, 138169, 139081, 141835, 142759, 143686, 145549, 146485, 147424, 148366, 149311, 150259, 153121, 154081, 155044, 156979, 157951, 158926, 159904, 160885, 161869, 163846, 164839, 165835, 168841, 169849, 170860, 171874, 172891, 173911, 174934, 176989, 178021, 180094, 181135, 182179, 184276, 185329, 186385, 189571, 190639, 191710, 192784, 193861, 194941, 197110, 198199, 199291, 201484, 202585, 203689, 207019.

Some larger examples :