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nonagonal n.  and  odious n.

First numbers that belong to both sets:

1, 261, 651, 750, 856, 1089, 1216, 1350, 1491, 1639, 2125, 3286, 3961, 4446, 4699, 4959, 5781, 6069, 6364, 6666, 7291, 8281, 9334, 10071, 11629, 12450, 12871, 14176, 15081, 16014, 16975, 18469, 20559, 21646, 23329, 23904, 25075, 25671, 26274, 26884, 28125, 30691, 32016, 32689, 35451, 38325, 39061, 40554, 41311, 43624, 47619, 48439, 50941, 53506, 54375, 55251, 56134, 58825, 60654, 65349, 66309, 67276, 68250, 70219, 73225, 79426, 82621, 83700, 86979, 88086, 90321, 91449, 97194, 100725, 104319, 109209, 110449, 111696, 115479, 119325, 120621, 129889, 131241, 135339, 139500, 145146, 148011, 150904, 158259, 159751, 171939, 175056, 179784, 182971, 187804, 194346, 197659, 199326, 202681, 204369, 214644, 216381, 228736, 232329, 235950, 237771, 241434, 245125, 246981, 250714, 252591, 254475, 262081, 264000, 269799, 273700, 275661, 277629, 283575, 285571, 287574, 295656, 303850, 305916, 307989, 310069, 312156, 314250, 316351, 324825, 326961, 331254, 333411, 337746, 339924, 344301, 346500, 348706, 350919, 353139, 355366, 357600, 359841, 362089, 373434, 378021, 380325, 382636, 389611, 396649, 410914, 415725, 422994, 445179, 447679, 450186, 455221, 457749, 460284, 465375, 470494, 475641, 480816, 483414, 488631, 493876, 496509, 499149, 504450, 512454, 515136, 517825, 520521, 531375, 542341, 545100, 556206, 561801, 567424, 570246, 573075, 590196, 595959, 610489, 619291, 628156, 631125, 655129, 658161, 664246, 670359, 682669, 695091, 698214, 701344, 704481, 707625, 713934, 717099, 723450, 736236, 742671, 745899, 752376, 755625, 758881, 762144, 765414, 768691, 778564, 781869, 788500, 791826, 805200, 818686, 822075, 835701, 849439, 856350, 866769, 891325, 898404, 901954, 905511, 909075, 912646, 923401, 930606, 934219, 959706, 963375, 970734, 989254, 996711, 1000450, 1007949, 1011709, 1023031, 1026819, 1038225, 1045864, 1049694, 1053531, 1057375, 1065084, 1072821, 1076700, 1080586, 1092286, 1096200, 1100121, 1104049, 1111926, 1115875, 1123794, 1127764, 1147719, 1151731, 1155750, 1163809, 1167849, 1175950, 1184079, 1196325, 1212751, 1221006, 1241766, 1254306, 1258500, 1279575, 1288054, 1305096, 1309374, 1313659, 1317951, 1330869, 1348191, 1352539, 1356894, 1361256.

Some larger examples :