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odious n.  and  pentagonal n.

First numbers that belong to both sets:

1, 22, 35, 70, 117, 145, 176, 247, 376, 425, 477, 532, 590, 651, 782, 852, 925, 1001, 1335, 1426, 1617, 1717, 2035, 2147, 2380, 2882, 3151, 3290, 3577, 3725, 4510, 5017, 5551, 6112, 6305, 6501, 6902, 7315, 8855, 10045, 10292, 10542, 10795, 11310, 11572, 11837, 12376, 12650, 13207, 13490, 13776, 14065, 15251, 15862, 16172, 16485, 16801, 17120, 18095, 18760, 19097, 20126, 21182, 21540, 23002, 23751, 24130, 24897, 25285, 26070, 26467, 26867, 27270, 27676, 28497, 28912, 29330, 29751, 30602, 32340, 33227, 33675, 34126, 35497, 35960, 36426, 36895, 38320, 39285, 39772, 41750, 42757, 43265, 43776, 44807, 46376, 47437, 47972, 49595, 50692, 51245, 54055, 55777, 58115, 58707, 59900, 60501, 63551, 64792, 65417, 66045, 67310, 69230, 69876, 73815, 76501, 78547, 82017, 82720, 84847, 85562, 86280, 88452, 91390, 93625, 94376, 95887, 98176, 98945, 99717, 101270, 102051, 102835, 104412, 105205, 107602, 109215, 110840, 113300, 114955, 117460, 119145, 119992, 120842, 121695, 122551, 123410, 124272, 125137, 127750, 131276, 132165, 133057, 133952, 134850, 135751, 139385, 143067, 144926, 146797, 150575, 155365, 159251, 161212, 163185, 164176, 165170, 171197, 172212, 173230, 174251, 176302, 177332, 178365, 180440, 181482, 187797, 189926, 190995, 193142, 194220, 196385, 199655, 201850, 202952, 204057, 205165, 207390, 209627, 214137, 217551, 219842, 220992, 222145, 229126, 230300, 232657, 238602, 239800, 241001, 243412, 247051, 248270, 251945, 255647, 258130, 261877, 265651, 266915, 268182, 269452, 274562, 275847, 278426, 281017, 283620, 284926, 288862, 295482, 296815, 298151, 300832, 306230, 308947, 310310, 311676, 315792, 317170, 318551, 322712, 329707, 335357, 338200, 341055, 346801, 351142, 352595, 354051, 355510, 358437, 361376, 364327, 367290, 373252, 377755, 380772, 382285, 386842, 389895, 391426, 394497, 396037, 399126, 400675, 402227, 405340, 406901, 410032, 413175, 416330, 422676, 424270, 425867, 435512, 438751, 440375, 442002, 443632, 446901, 448540, 450182, 458437, 460097, 463426, 466767, 468442, 470120, 473485, 490490, 492207.

Some larger examples :