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arithmetic n.  and  centered pentagonal n.

First numbers that belong to both sets:

1, 6, 31, 51, 141, 181, 276, 331, 391, 456, 526, 601, 681, 766, 951, 1051, 1266, 1381, 1501, 1626, 1891, 2031, 2326, 2481, 2641, 2806, 2976, 3151, 3331, 3516, 3901, 4101, 4731, 4951, 5176, 5406, 5641, 5881, 6126, 6631, 6891, 7426, 7701, 7981, 8556, 8851, 9151, 9766, 10081, 10401, 10726, 11391, 11731, 12426, 12781, 13141, 13506, 14251, 14631, 15406, 15801, 16201, 16606, 17431, 17851, 18276, 18706, 19141, 19581, 20026, 20931, 21391, 21856, 22326, 22801, 23281, 23766, 24751, 25251, 25756, 26266, 26781, 27301, 28356, 28891, 29431, 30526, 31081, 31641, 32206, 33351, 33931, 35106, 35701, 36301, 36906, 37516, 38131, 38751, 40006, 40641, 41281, 41926, 43231, 43891, 44556, 45901, 46581, 48651, 49351, 50766, 51481, 52201, 52926, 54391, 55131, 56626, 57381, 58141, 59676, 60451, 61231, 62806, 63601, 64401, 65206, 66016, 66831, 67651, 68476, 69306, 70141, 70981, 71826, 74391, 75256, 76126, 77001, 77881, 78766, 79656, 80551, 81451, 82356, 83266, 84181, 85101, 87891, 88831, 90726, 91681, 92641, 93606, 95551, 96531, 99501, 100501, 102516, 103531, 104551, 105576, 106606, 107641, 108681, 109726, 111831, 112891, 115026, 116101, 117181, 118266, 119356, 120451, 121551, 123766, 124881, 126001, 127126, 129391, 130531, 131676, 133981, 135141, 136306, 138651, 139831, 142206, 143401, 144601, 145806, 147016, 148231, 149451, 151906, 153141, 154381, 156876, 158131, 159391, 161926, 163201, 164481, 165766, 168351, 169651, 172266, 173581, 174901, 176226, 180231, 182926, 184281, 185641, 187006, 188376, 189751, 191131, 192516, 195301, 196701, 200931, 202351, 205206, 206641, 208081, 209526, 210976, 212431, 213891, 215356, 218301, 219781, 222756, 224251, 225751, 228766, 230281, 231801, 233326, 234856, 236391, 237931, 239476, 241026, 242581, 244141, 245706, 248851, 250431, 252016, 253606, 255201, 256801, 258406, 261631, 263251, 264876, 268141, 269781, 273076, 274731, 276391, 279726, 281401, 283081, 284766, 288151, 289851, 293266, 294981, 296701, 300156, 301891, 303631, 305376, 307126, 308881, 310641, 312406, 315951.

Some larger examples :