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centered triangular n.  and  deficient n.

First numbers that belong to both sets:

1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 514, 571, 631, 694, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2710, 2839, 2971, 3106, 3244, 3385, 3529, 3676, 3826, 3979, 4135, 4294, 4456, 4621, 4789, 5134, 5311, 5491, 5674, 6049, 6241, 6436, 6634, 6835, 7039, 7246, 7456, 7669, 7885, 8104, 8326, 8551, 8779, 9010, 9244, 9481, 9721, 9964, 10210, 10459, 10711, 10966, 11224, 11485, 11749, 12016, 12286, 12559, 12835, 13114, 13396, 13681, 13969, 14554, 14851, 15151, 15454, 16069, 16381, 16696, 17014, 17335, 17659, 17986, 18316, 18649, 18985, 19324, 19666, 20011, 20359, 20710, 21064, 21421, 21781, 22510, 22879, 23251, 23626, 24004, 24385, 24769, 25156, 25546, 25939, 26335, 26734, 27541, 27949, 28774, 29191, 29611, 30034, 30889, 31321, 31756, 32194, 32635, 33079, 33526, 33976, 34429, 34885, 35344, 35806, 36271, 36739, 37210, 37684, 38161, 38641, 39124, 39610, 40099, 40591, 41086, 42085, 42589, 43096, 43606, 44119, 44635, 45154, 45676, 46201, 46729, 47794, 48331, 48871, 49414, 50509, 51061, 51616, 52174, 52735, 53299, 53866, 54436, 55009, 55585, 56164, 56746, 57331, 57919, 58510, 59104, 59701, 60301, 60904, 61510, 62119, 62731, 63346, 63964, 64585, 65209, 65836, 66466, 67099, 67735, 68374, 69016, 69661, 70309, 71614, 72271, 72931, 73594, 74929, 75601, 76276, 76954, 77635, 78319, 79006, 80389, 81085, 81784, 82486, 83191, 83899, 84610, 85324, 86041, 86761, 87484, 88210, 88939, 89671, 90406, 91144, 91885, 92629, 93376, 94126, 94879, 95635, 96394, 97156, 97921, 98689, 100234, 101011, 101791, 102574, 104149, 104941, 105736, 106534, 107335, 108139, 108946, 109756, 110569, 111385, 112204, 113026, 113851, 114679, 115510, 116344, 117181, 118021, 119710, 120559, 121411, 122266, 123124, 123985, 124849, 125716, 126586, 127459, 128335, 129214, 130096, 130981, 131869, 133654, 134551, 135451.

Some larger examples :