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centered nonagonal n.  and  odious n.

First numbers that belong to both sets:

1, 28, 55, 91, 253, 406, 496, 595, 820, 1081, 1225, 1378, 1540, 1891, 2485, 3160, 3403, 3655, 3916, 4186, 4753, 5356, 5671, 5995, 7021, 7750, 8128, 8515, 9316, 10585, 11476, 12403, 12880, 13366, 13861, 14365, 17020, 18145, 18721, 19900, 21115, 21736, 24310, 24976, 25651, 26335, 27028, 27730, 28441, 29161, 29890, 30628, 32131, 34453, 38503, 41041, 43660, 46360, 47278, 48205, 49141, 51040, 53956, 56953, 58996, 63190, 64261, 65341, 66430, 67528, 68635, 72010, 74305, 76636, 77815, 79003, 80200, 81406, 82621, 88831, 91378, 92665, 93961, 95266, 97903, 104653, 111628, 114481, 118828, 123256, 124750, 126253, 129286, 130816, 132355, 135460, 137026, 138601, 143380, 144991, 148240, 149878, 151525, 154846, 159895, 161596, 168490, 171991, 173755, 175528, 184528, 186355, 188191, 190036, 193753, 201295, 203203, 205120, 210925, 214840, 218791, 220780, 224785, 228826, 230860, 232903, 234955, 237016, 243253, 251695, 253828, 258121, 262450, 264628, 266815, 269011, 271216, 273430, 280126, 282376, 286903, 289180, 293761, 296065, 300700, 303031, 319600, 322003, 324415, 326836, 329266, 331705, 339076, 341551, 344035, 346528, 351541, 356590, 359128, 361675, 364231, 366796, 371953, 377146, 379756, 385003, 390286, 392941, 398278, 400960, 406351, 409060, 414505, 425503, 431056, 439453, 445096, 447931, 450775, 459361, 462241, 468028, 470935, 476776, 482653, 485605, 491536, 500500, 509545, 512578, 515620, 521731, 530965, 543403, 546535, 555985, 571915, 581581, 584821, 591328, 597871, 601156, 607753, 611065, 614386, 617716, 621055, 624403, 627760, 631126, 644680, 651511, 654940, 658378, 661825, 672220, 675703, 679195, 682696, 693253, 700336, 711028, 718201, 729028, 747253, 754606, 761995, 780625, 803278, 807085, 818560, 830116, 841753, 845650, 849556, 861328, 865270, 877150, 881128, 885115, 901153, 905185, 913276, 933661, 937765, 941878, 946000, 950131, 958420, 966745, 979300, 983503, 987715, 996166, 1008910, 1013176, 1021735, 1030330, 1034641, 1038961, 1047628, 1056331, 1060696, 1065070, 1073845, 1078246, 1082656, 1087075, 1095940, 1104841, 1109305, 1122751, 1154440, 1159003, 1172746, 1181953, 1191196, 1195831, 1209790, 1214461.

Some larger examples :