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cyclic n.  and  plaindrome

First numbers that belong to both sets:

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 33, 35, 37, 47, 59, 67, 69, 77, 79, 89, 113, 115, 119, 123, 127, 133, 137, 139, 145, 149, 157, 159, 167, 177, 179, 199, 223, 227, 229, 233, 235, 239, 247, 249, 255, 257, 259, 267, 269, 277, 299, 335, 337, 339, 345, 347, 349, 359, 367, 377, 379, 389, 445, 447, 449, 455, 457, 467, 469, 479, 499, 557, 559, 569, 577, 589, 599, 667, 677, 679, 699, 779, 789, 799, 899, 1111, 1115, 1117, 1123, 1129, 1133, 1135, 1139, 1145, 1147, 1149, 1157, 1159, 1167, 1169, 1177, 1189, 1199, 1223, 1229, 1235, 1237, 1245, 1247, 1249, 1257, 1259, 1267, 1277, 1279, 1289, 1333, 1335, 1337, 1339, 1345, 1347, 1349, 1357, 1367, 1399, 1447, 1457, 1459, 1469, 1479, 1489, 1499, 1559, 1567, 1577, 1579, 1589, 1667, 1669, 1679, 1689, 1699, 1777, 1779, 1789, 1799, 1889, 1999, 2227, 2229, 2235, 2237, 2239, 2245, 2249, 2257, 2267, 2269, 2279, 2333, 2335, 2339, 2345, 2347, 2357, 2369, 2377, 2389, 2399, 2447, 2449, 2459, 2467, 2477, 2479, 2489, 2555, 2557, 2567, 2569, 2579, 2589, 2599, 2669, 2677, 2689, 2699, 2777, 2779, 2789, 2899, 2999, 3333, 3335, 3337, 3347, 3349, 3359, 3367, 3377, 3379, 3389, 3449, 3457, 3467, 3469, 3489, 3499, 3557, 3559, 3567, 3569, 3579, 3589, 3599, 3667, 3669, 3677, 3679, 3689, 3777, 3779, 3799, 3889, 3899, 4447, 4457, 4469, 4479, 4499, 4559, 4567, 4569, 4577, 4579, 4589, 4667, 4677, 4679, 4699, 4777, 4789, 4799, 4889, 4899, 4999, 5557, 5567, 5569, 5579, 5599, 5667, 5669, 5677, 5689, 5699, 5777, 5779, 5899, 5999, 6667, 6677, 6679, 6689, 6779, 6799, 6899, 6999, 7777, 7789, 7799, 7899, 7999, 8889, 8899, 8999, 11111.

Some larger examples :