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Duffinian n.  and  odious n.

First numbers that belong to both sets:

4, 8, 16, 21, 25, 32, 35, 49, 50, 55, 64, 81, 93, 98, 100, 115, 121, 128, 133, 143, 155, 161, 171, 185, 203, 205, 217, 242, 247, 253, 256, 259, 265, 279, 289, 299, 301, 309, 319, 324, 327, 333, 341, 351, 355, 361, 381, 385, 391, 392, 400, 403, 415, 425, 451, 453, 471, 481, 484, 493, 505, 511, 512, 515, 517, 527, 529, 535, 539, 551, 565, 575, 578, 583, 589, 595, 597, 611, 623, 625, 635, 651, 671, 687, 689, 707, 713, 721, 722, 731, 737, 749, 755, 767, 779, 781, 784, 793, 799, 800, 803, 805, 815, 817, 835, 837, 841, 849, 865, 871, 875, 889, 899, 901, 905, 913, 923, 925, 935, 939, 949, 959, 961, 968, 979, 981, 985, 1007, 1024, 1027, 1029, 1047, 1053, 1057, 1058, 1067, 1075, 1081, 1089, 1099, 1101, 1119, 1135, 1137, 1143, 1147, 1156, 1159, 1165, 1177, 1183, 1189, 1207, 1211, 1219, 1225, 1243, 1250, 1255, 1261, 1273, 1281, 1296, 1299, 1315, 1317, 1349, 1359, 1371, 1387, 1389, 1397, 1407, 1411, 1413, 1417, 1444, 1461, 1465, 1497, 1507, 1513, 1519, 1533, 1537, 1555, 1573, 1577, 1585, 1591, 1600, 1603, 1623, 1629, 1633, 1639, 1643, 1645, 1651, 1673, 1679, 1681, 1682, 1687, 1691, 1703, 1727, 1735, 1739, 1763, 1765, 1769, 1775, 1807, 1809, 1819, 1821, 1825, 1835, 1837, 1843, 1849, 1855, 1857, 1875, 1893, 1897, 1903, 1915, 1921, 1922, 1927, 1936, 1939, 1955, 1957, 1961, 1967, 1969, 1981, 2007, 2023, 2035, 2041, 2047, 2048, 2057, 2071, 2075, 2077, 2101, 2105, 2116, 2119, 2123, 2125, 2133, 2159, 2171, 2173, 2177, 2183, 2187, 2189, 2197, 2201, 2217, 2231, 2249, 2255, 2257, 2263, 2279, 2285, 2291, 2303, 2305, 2312, 2315, 2317.

Some larger examples :