Search a number
alternating n.  and  economical n.

First numbers that belong to both sets:

1, 2, 3, 5, 7, 10, 14, 16, 21, 23, 25, 27, 29, 32, 41, 43, 47, 49, 61, 67, 81, 83, 89, 101, 103, 105, 107, 109, 121, 123, 125, 127, 129, 141, 145, 147, 149, 161, 163, 167, 169, 181, 183, 185, 189, 250, 256, 301, 305, 307, 329, 343, 347, 349, 361, 365, 367, 383, 389, 503, 509, 521, 523, 529, 541, 547, 563, 567, 569, 581, 587, 701, 709, 727, 729, 743, 761, 769, 787, 896, 907, 929, 941, 947, 961, 967, 983, 1018, 1058, 1072, 1094, 1214, 1216, 1234, 1238, 1250, 1294, 1296, 1418, 1438, 1454, 1458, 1472, 1478, 1618, 1654, 1658, 1678, 1696, 1814, 1838, 1856, 1858, 1874, 1894, 2103, 2105, 2107, 2125, 2127, 2129, 2141, 2143, 2149, 2161, 2165, 2181, 2183, 2187, 2303, 2305, 2307, 2309, 2341, 2345, 2347, 2349, 2361, 2381, 2383, 2389, 2501, 2503, 2521, 2523, 2527, 2543, 2545, 2549, 2569, 2581, 2589, 2701, 2705, 2707, 2721, 2723, 2729, 2741, 2747, 2749, 2765, 2767, 2785, 2787, 2789, 2901, 2903, 2905, 2909, 2923, 2927, 2947, 2949, 2963, 2965, 2969, 2989, 3072, 3430, 3456, 3698, 4105, 4107, 4109, 4127, 4129, 4145, 4183, 4187, 4189, 4307, 4327, 4349, 4361, 4363, 4385, 4501, 4507, 4523, 4529, 4547, 4549, 4561, 4567, 4583, 4703, 4705, 4721, 4723, 4729, 4765, 4781, 4783, 4787, 4789, 4903, 4907, 4909, 4941, 4943, 4963, 4967, 4969, 4985, 4987, 5056, 5618, 5632, 5696, 5832, 6101, 6121, 6125, 6143, 6163, 6167, 6181, 6301, 6323, 6329, 6343, 6349, 6361, 6367, 6389, 6503, 6521, 6529, 6547, 6561, 6563, 6569, 6581, 6587, 6701, 6703, 6709, 6723, 6727, 6761, 6763, 6769, 6781, 6907, 6947, 6949, 6961, 6967, 6983, 7290, 8101, 8123, 8125, 8147, 8161, 8167, 8329, 8363, 8369.

Some larger examples :