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balanced n.  and  odious n.

First numbers that belong to both sets:

2, 11, 19, 21, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 266, 268, 290, 302, 304, 316, 348, 410, 412, 416, 426, 434, 460, 468, 502, 508, 518, 524, 527, 532, 535, 539, 541, 542, 551, 552, 555, 557, 558, 563, 565, 566, 569, 570, 572, 578, 583, 587, 589, 590, 595, 597, 598, 601, 602, 604, 611, 613, 614, 617, 618, 620, 625, 626, 628, 632, 647, 651, 653, 654, 659, 661, 662, 665, 666, 668, 675, 677, 678, 681, 682, 684, 689, 690, 692, 696, 707, 709, 710, 713, 714, 716, 721, 722, 724, 728, 737, 738, 740, 744, 752, 775, 779, 781, 782, 787, 789, 790, 793, 794, 796, 803, 805, 806, 809, 810, 812, 817, 818, 820, 824, 835, 837, 838, 841, 842, 844, 849, 850, 852, 856, 865, 866, 868, 872, 880, 899, 901, 902, 905, 906, 908, 913, 914, 916, 920, 929, 930, 932, 936, 944, 954, 961, 962, 964, 968, 976, 992, 1022, 1054, 1070, 1102, 1110, 1138, 1178, 1190, 1202, 1294, 1398, 1454, 1634, 1646, 1654, 1670, 1730, 1766, 1778, 1790, 1826, 1922, 1934, 1946, 1982, 2014, 2054, 2102, 2134, 2154, 2226, 2386, 2402, 2426, 2538, 2558, 2582, 2586, 2642, 2678, 2766, 2778, 2790, 2826, 2882, 2902, 2930, 6695, 6713, 6719, 6721, 6767, 6775, 6791, 6857, 6875, 6881, 6911, 6947, 6959, 6991, 7027, 7039, 7091, 7097, 7115, 7117, 7123, 7145, 7151, 7153, 7163, 7197, 7201, 7225, 7231, 7243, 7251, 7257, 7267, 7273, 7343, 7369, 7445, 7449, 7503, 7511, 7517, 7521, 7527, 7595, 7715, 7767, 7801, 7811, 7823, 7835, 7837, 7841, 7851, 7865, 7913, 7945, 7953, 7959, 7993, 8001, 8071, 8089, 8095, 8123, 8125, 8151, 8161, 8173, 8195, 8197, 8215.

Some larger examples :