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cyclic n.  and  deceptive n.

First numbers that belong to both sets:

91, 259, 451, 481, 703, 1729, 2821, 2981, 3367, 4141, 4187, 5461, 6533, 6541, 6601, 7471, 7777, 8149, 8401, 8911, 10001, 11111, 12403, 13981, 14701, 14911, 15211, 15841, 21931, 22321, 24013, 24661, 27613, 29341, 34133, 34441, 35113, 38503, 41041, 45527, 46657, 48433, 50851, 50881, 52633, 54913, 57181, 63139, 63973, 65311, 66991, 67861, 68101, 75361, 79003, 82513, 83119, 94139, 95161, 97273, 97681, 100001, 101101, 101491, 102173, 108691, 113201, 115627, 115921, 118301, 118957, 122221, 126217, 128713, 130351, 131821, 134821, 134863, 137137, 137149, 138481, 139231, 145181, 147001, 148417, 152551, 158497, 162401, 164761, 166499, 172081, 179881, 188191, 188269, 188461, 188501, 196651, 201917, 216001, 216931, 225589, 226273, 229633, 231337, 234421, 237817, 245491, 247753, 248677, 250717, 251251, 252601, 253099, 269011, 269569, 274231, 281821, 286903, 287749, 287809, 294409, 298033, 301081, 302177, 304057, 314821, 334153, 340561, 341503, 346801, 351809, 357641, 364277, 366337, 372731, 385003, 390313, 391141, 399001, 401401, 410041, 413339, 420343, 437251, 451091, 455971, 458641, 463241, 463489, 481601, 488881, 489997, 491063, 492101, 497377, 497503, 497927, 505363, 507529, 509971, 511969, 512461, 520801, 522349, 530881, 532171, 552721, 567721, 585631, 586993, 588193, 589537, 597871, 601657, 603961, 607321, 632641, 634351, 642001, 658801, 665401, 670033, 679861, 710533, 721801, 736291, 741751, 748657, 749521, 754369, 764491, 765703, 827281, 838201, 841633, 847693, 852841, 853381, 868001, 873181, 880237, 886033, 903169, 906193, 909709, 924001, 929633, 963857, 974611, 976873, 981317, 989017, 997633, 997981, 999001, 1004329, 1024651, 1033669, 1039441, 1039849, 1041043, 1042417, 1056331, 1069993, 1080697, 1081649, 1082809, 1090051, 1096681, 1111111, 1128871, 1141141, 1146401, 1152271, 1163801, 1168513, 1169101, 1182721, 1193221, 1242241, 1242571, 1251949, 1267801, 1268551, 1272271, 1275347, 1294411, 1306369, 1336699, 1362061, 1376299, 1394171, 1398101, 1408849, 1419607, 1446241, 1446661, 1450483, 1461241, 1462441, 1463749, 1492663, 1498981, 1504321, 1531711, 1543381, 1551941, 1569457, 1576381, 1583821, 1590751, 1602601, 1615681, 1703221, 1705621, 1708993, 1711381, 1711601, 1719601, 1731241.

Some larger examples :