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centered pentagonal n.  and  odious n.

First numbers that belong to both sets:

1, 16, 31, 76, 181, 276, 331, 391, 601, 681, 856, 1051, 1156, 1756, 1891, 2326, 2641, 2976, 3151, 3331, 3901, 4101, 4306, 4516, 5176, 5406, 5641, 5881, 6631, 6891, 7156, 7426, 7701, 7981, 10081, 10401, 11731, 12426, 12781, 13876, 15016, 16201, 16606, 17851, 18276, 18706, 19141, 19581, 20476, 20931, 21391, 22326, 23281, 23766, 24256, 25251, 25756, 28891, 29431, 29976, 30526, 31081, 32206, 34516, 35106, 35701, 36301, 36906, 38131, 38751, 39376, 40006, 41281, 44556, 45226, 45901, 46581, 47266, 47956, 48651, 49351, 51481, 52926, 53656, 55131, 55876, 56626, 58141, 63601, 66016, 66831, 67651, 68476, 69306, 70981, 72676, 73531, 75256, 76126, 77881, 82356, 85101, 86026, 86956, 88831, 89776, 91681, 92641, 96531, 97516, 100501, 102516, 103531, 104551, 107641, 108681, 111831, 113956, 115026, 117181, 119356, 120451, 122656, 123766, 124881, 126001, 127126, 128256, 129391, 130531, 133981, 136306, 137476, 142206, 144601, 145806, 148231, 150676, 151906, 153141, 154381, 163201, 164481, 176226, 177556, 178891, 181576, 182926, 185641, 189751, 191131, 193906, 196701, 198106, 199516, 202351, 203776, 206641, 208081, 212431, 215356, 218301, 219781, 221266, 228766, 234856, 239476, 241026, 242581, 245706, 247276, 248851, 252016, 258406, 261631, 264876, 266506, 271426, 276391, 281401, 284766, 286456, 291556, 293266, 294981, 296701, 300156, 301891, 305376, 308881, 310641, 314176, 317731, 319516, 323101, 330331, 333976, 335806, 339481, 346891, 350626, 354381, 360051, 365766, 369601, 373456, 375391, 377331, 379276, 381226, 383181, 389076, 391051, 399001, 407031, 409051, 421276, 423331, 427456, 429526, 431601, 433681, 437856, 450501, 454756, 456891, 461176, 463326, 465481, 469806, 474151, 485101, 491731, 493951, 505126, 507376, 511891, 514156, 525556, 534766, 541726, 548731, 551076, 553426, 555781, 565251, 570016, 572406, 584431, 589276, 591706, 594141, 596581, 603931, 606391, 611326, 613801, 616281, 618766, 628756, 631266, 636301, 638826, 641356, 643891, 646431, 648976, 651526, 656641, 677301, 690376, 693006, 695641, 698281, 700926, 722266, 733056, 738481, 741201, 743926.

Some larger examples :