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amenable n.  and  plaindrome

First numbers that belong to both sets:

1, 5, 8, 9, 12, 13, 16, 17, 24, 25, 28, 29, 33, 36, 37, 44, 45, 48, 49, 56, 57, 68, 69, 77, 88, 89, 112, 113, 116, 117, 124, 125, 128, 129, 133, 136, 137, 144, 145, 148, 149, 156, 157, 168, 169, 177, 188, 189, 224, 225, 228, 229, 233, 236, 237, 244, 245, 248, 249, 256, 257, 268, 269, 277, 288, 289, 333, 336, 337, 344, 345, 348, 349, 356, 357, 368, 369, 377, 388, 389, 444, 445, 448, 449, 456, 457, 468, 469, 477, 488, 489, 556, 557, 568, 569, 577, 588, 589, 668, 669, 677, 688, 689, 777, 788, 789, 888, 889, 1112, 1113, 1116, 1117, 1124, 1125, 1128, 1129, 1133, 1136, 1137, 1144, 1145, 1148, 1149, 1156, 1157, 1168, 1169, 1177, 1188, 1189, 1224, 1225, 1228, 1229, 1233, 1236, 1237, 1244, 1245, 1248, 1249, 1256, 1257, 1268, 1269, 1277, 1288, 1289, 1333, 1336, 1337, 1344, 1345, 1348, 1349, 1356, 1357, 1368, 1369, 1377, 1388, 1389, 1444, 1445, 1448, 1449, 1456, 1457, 1468, 1469, 1477, 1488, 1489, 1556, 1557, 1568, 1569, 1577, 1588, 1589, 1668, 1669, 1677, 1688, 1689, 1777, 1788, 1789, 1888, 1889, 2224, 2225, 2228, 2229, 2233, 2236, 2237, 2244, 2245, 2248, 2249, 2256, 2257, 2268, 2269, 2277, 2288, 2289, 2333, 2336, 2337, 2344, 2345, 2348, 2349, 2356, 2357, 2368, 2369, 2377, 2388, 2389, 2444, 2445, 2448, 2449, 2456, 2457, 2468, 2469, 2477, 2488, 2489, 2556, 2557, 2568, 2569, 2577, 2588, 2589, 2668, 2669, 2677, 2688, 2689, 2777, 2788, 2789, 2888, 2889, 3333, 3336, 3337, 3344, 3345, 3348, 3349, 3356, 3357, 3368, 3369, 3377, 3388, 3389, 3444, 3445, 3448, 3449, 3456, 3457, 3468, 3469, 3477, 3488, 3489, 3556, 3557, 3568, 3569, 3577.

Some larger examples :