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Search a number
alternating n.  and  amenable n.

First numbers that belong to both sets:

1, 5, 8, 9, 12, 16, 21, 25, 29, 32, 36, 41, 45, 49, 52, 56, 61, 65, 69, 72, 76, 81, 85, 89, 92, 96, 101, 105, 109, 121, 125, 129, 141, 145, 149, 161, 165, 169, 181, 185, 189, 212, 216, 232, 236, 252, 256, 272, 276, 292, 296, 301, 305, 309, 321, 325, 329, 341, 345, 349, 361, 365, 369, 381, 385, 389, 412, 416, 432, 436, 452, 456, 472, 476, 492, 496, 501, 505, 509, 521, 525, 529, 541, 545, 549, 561, 565, 569, 581, 585, 589, 612, 616, 632, 636, 652, 656, 672, 676, 692, 696, 701, 705, 709, 721, 725, 729, 741, 745, 749, 761, 765, 769, 781, 785, 789, 812, 816, 832, 836, 852, 856, 872, 876, 892, 896, 901, 905, 909, 921, 925, 929, 941, 945, 949, 961, 965, 969, 981, 985, 989, 1012, 1016, 1032, 1036, 1052, 1056, 1072, 1076, 1092, 1096, 1212, 1216, 1232, 1236, 1252, 1256, 1272, 1276, 1292, 1296, 1412, 1416, 1432, 1436, 1452, 1456, 1472, 1476, 1492, 1496, 1612, 1616, 1632, 1636, 1652, 1656, 1672, 1676, 1692, 1696, 1812, 1816, 1832, 1836, 1852, 1856, 1872, 1876, 1892, 1896, 2101, 2105, 2109, 2121, 2125, 2129, 2141, 2145, 2149, 2161, 2165, 2169, 2181, 2185, 2189, 2301, 2305, 2309, 2321, 2325, 2329, 2341, 2345, 2349, 2361, 2365, 2369, 2381, 2385, 2389, 2501, 2505, 2509, 2521, 2525, 2529, 2541, 2545, 2549, 2561, 2565, 2569, 2581, 2585, 2589, 2701, 2705, 2709, 2721, 2725, 2729, 2741, 2745, 2749, 2761, 2765, 2769, 2781, 2785, 2789, 2901, 2905, 2909, 2921, 2925, 2929, 2941, 2945, 2949, 2961, 2965, 2969, 2981, 2985, 2989, 3012, 3016, 3032, 3036, 3052, 3056, 3072, 3076, 3092, 3096, 3212, 3216, 3232, 3236.

Some larger examples :