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binomial coefficient  and  odious n.

First numbers that belong to both sets:

21, 28, 35, 55, 56, 70, 84, 91, 171, 220, 253, 276, 286, 351, 364, 406, 465, 496, 560, 595, 666, 820, 861, 1001, 1081, 1140, 1225, 1287, 1330, 1378, 1431, 1485, 1540, 1653, 1770, 1891, 2002, 2024, 2211, 2300, 2346, 2380, 2485, 2850, 3003, 3160, 3240, 3403, 3655, 3916, 4060, 4186, 4368, 4371, 4495, 4560, 4753, 4950, 4960, 5005, 5151, 5253, 5356, 5456, 5565, 5671, 5985, 5995, 6105, 6188, 6786, 7021, 7260, 7315, 7503, 7750, 8001, 8008, 8128, 8515, 8778, 8855, 9045, 9316, 9591, 9870, 10296, 10440, 10585, 10626, 10731, 10878, 11175, 11476, 11480, 12090, 12376, 12403, 12561, 12650, 12880, 13244, 13366, 13695, 13861, 14196, 14365, 15051, 16110, 16215, 16290, 16653, 16836, 17020, 17205, 17296, 17766, 18145, 18424, 18721, 19110, 19448, 19600, 19701, 19900, 20301, 20349, 20825, 21115, 21321, 21528, 21736, 21945, 22100, 22791, 23426, 23751, 23871, 24310, 24531, 24976, 25425, 25651, 25878, 26335, 26565, 26796, 27028, 27730, 28203, 28441, 29161, 29260, 29890, 30135, 30628, 31125, 31626, 31824, 32131, 32509, 33411, 33649, 33930, 34220, 34453, 34980, 35511, 35778, 35960, 35990, 36585, 37820, 38226, 38503, 38781, 41041, 41616, 41664, 42504, 43071, 43660, 43956, 44850, 45753, 46056, 46360, 46376, 47278, 47586, 48205, 48620, 48828, 49141, 49770, 50116, 50388, 51040, 51360, 52650, 53130, 53301, 53628, 53956, 54285, 54740, 56953, 58653, 58996, 59640, 60378, 61776, 62481, 62835, 63190, 63546, 64261, 64980, 65341, 66045, 66430, 67161, 67528, 68265, 68635, 70125, 70300, 70500, 71631, 72010, 72771, 73150, 73536, 73815, 74305, 74613, 75078, 76076, 76245, 76636, 77815, 79003, 80200, 81406, 82215, 82251, 82621, 83436, 84255, 84666, 85320, 85491, 85905, 86736, 87990, 88410, 88560, 88831, 89253, 89676, 90525, 90951, 91378, 91390, 92378, 92665, 93096, 93528, 93961, 95266, 96141, 97461, 97903, 98346, 98770, 99681, 101025, 101270, 102340, 102378.

Some larger examples :