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Search a number
alternating n.  and  odious n.

First numbers that belong to both sets:

1, 2, 4, 7, 8, 14, 16, 21, 25, 32, 38, 41, 47, 49, 50, 52, 56, 61, 67, 69, 70, 74, 76, 81, 87, 94, 98, 103, 107, 109, 121, 127, 143, 145, 161, 167, 181, 185, 214, 218, 230, 234, 236, 254, 256, 274, 276, 290, 292, 296, 301, 307, 309, 321, 327, 341, 345, 361, 367, 369, 381, 385, 410, 412, 416, 434, 436, 454, 458, 472, 478, 494, 496, 501, 505, 521, 527, 529, 541, 545, 563, 565, 569, 583, 587, 589, 614, 618, 632, 638, 654, 656, 672, 678, 690, 692, 696, 701, 707, 709, 721, 727, 743, 747, 749, 761, 767, 769, 781, 787, 789, 810, 812, 818, 830, 832, 838, 850, 852, 856, 872, 878, 890, 892, 896, 901, 905, 923, 925, 929, 941, 947, 949, 961, 967, 981, 985, 1010, 1012, 1016, 1030, 1034, 1036, 1054, 1058, 1070, 1072, 1078, 1090, 1092, 1096, 1214, 1216, 1234, 1236, 1250, 1252, 1256, 1270, 1274, 1276, 1294, 1296, 1414, 1418, 1432, 1438, 1454, 1456, 1474, 1476, 1494, 1498, 1610, 1612, 1618, 1630, 1634, 1636, 1654, 1658, 1670, 1674, 1676, 1694, 1698, 1810, 1812, 1816, 1832, 1838, 1850, 1852, 1858, 1870, 1872, 1878, 1894, 1898, 2101, 2105, 2123, 2125, 2143, 2147, 2149, 2161, 2167, 2183, 2187, 2189, 2303, 2305, 2323, 2325, 2329, 2341, 2345, 2363, 2365, 2383, 2385, 2503, 2507, 2509, 2521, 2527, 2543, 2545, 2561, 2567, 2581, 2585, 2703, 2705, 2721, 2727, 2741, 2745, 2763, 2765, 2783, 2787, 2789, 2901, 2905, 2921, 2927, 2929, 2941, 2945, 2963, 2965, 2969, 2981, 2985, 3014, 3018, 3032, 3038, 3054, 3056, 3074, 3076, 3094, 3098, 3210, 3212, 3218, 3230, 3234, 3236, 3254, 3258, 3272, 3278, 3290, 3292, 3296, 3414.

Some larger examples :