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cyclic n.  and  Lehmer n.

First numbers that belong to both sets:

15, 51, 85, 91, 133, 247, 255, 259, 435, 451, 481, 511, 561, 595, 679, 703, 763, 771, 949, 1105, 1111, 1141, 1261, 1285, 1351, 1387, 1417, 1615, 1695, 1729, 1843, 1891, 2047, 2071, 2091, 2119, 2431, 2465, 2509, 2701, 2761, 2821, 2955, 3031, 3097, 3145, 3277, 3367, 3409, 3589, 3655, 3667, 3855, 4033, 4039, 4141, 4369, 4411, 4681, 4795, 4921, 5083, 5151, 5383, 5461, 5551, 5611, 5629, 5713, 6031, 6205, 6331, 6601, 6643, 6735, 7051, 7081, 7141, 7471, 7501, 7735, 7957, 8071, 8119, 8227, 8245, 8401, 8481, 8695, 8827, 8911, 8995, 9061, 9079, 9139, 9211, 9253, 9265, 9367, 9605, 9709, 9919, 9997, 10213, 10291, 10573, 10585, 10795, 10963, 11041, 11155, 11305, 11899, 12403, 12801, 12901, 13021, 13107, 13333, 13651, 13741, 13747, 13855, 13981, 14089, 14491, 14497, 14611, 14701, 14833, 14911, 14989, 15051, 15181, 15211, 15811, 15841, 16021, 16297, 16405, 16441, 16471, 16531, 16705, 16745, 16771, 16861, 17563, 17611, 17733, 17767, 18019, 18031, 18151, 18631, 18721, 18745, 18907, 18967, 19345, 19669, 19951, 20419, 20451, 20595, 20995, 21037, 21349, 21679, 21845, 21907, 21931, 22015, 22261, 22321, 22359, 23001, 23281, 23959, 24199, 24415, 24643, 24661, 24727, 24871, 25123, 25141, 25351, 25669, 26281, 26335, 26467, 26599, 26923, 27223, 27331, 27511, 27721, 28231, 28453, 28645, 28939, 29341, 30481, 30583, 30889, 31171, 31417, 31459, 31609, 31611, 31621, 32215, 32407, 32551, 32691, 33001, 33709, 34441, 34861, 35113, 35371, 35551, 35881, 36091, 36391, 36499, 36661, 36751, 36805, 37231, 37921, 37969, 38165, 38503, 39091, 39403, 39491, 39817, 39831, 39865, 40261, 40501, 40885, 40921, 41041, 41245, 41395, 41881, 42001, 42121, 42127, 42217, 42661, 42799, 43165, 43387, 43435, 43621, 44011, 44317, 44941, 45551, 45811, 45991, 46657, 47055, 47197, 47239, 47545, 47671, 47989, 48133, 48709, 49045, 49051, 49141, 49155, 49231, 49267.

Some larger examples :