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cyclic n.  and  Moran n.

First numbers that belong to both sets:

133, 209, 247, 407, 481, 511, 629, 803, 1141, 1387, 1417, 1651, 1679, 1853, 2119, 2159, 2353, 2771, 3031, 3077, 3097, 3383, 3439, 3523, 3749, 3781, 4577, 4607, 5149, 5161, 5833, 6331, 6443, 7033, 7361, 7501, 7543, 7859, 8203, 8227, 8717, 9253, 10109, 10213, 10279, 10307, 10543, 10727, 10963, 11647, 12563, 13111, 13117, 14093, 14099, 14383, 14521, 15409, 15689, 15751, 17153, 17461, 17777, 17803, 17887, 18071, 18299, 18653, 19171, 19601, 20137, 20197, 20371, 20603, 21073, 21541, 21743, 21907, 22009, 22049, 22249, 22711, 22793, 23413, 24191, 24449, 24643, 24803, 25691, 25699, 26221, 26333, 26519, 26933, 27037, 27721, 28489, 28739, 29417, 29431, 29831, 30617, 30701, 30901, 31483, 31841, 32071, 32167, 32729, 33007, 33193, 33241, 33557, 33959, 34219, 34411, 34901, 35513, 35627, 37043, 37283, 38323, 39649, 40007, 40027, 40201, 40403, 40409, 40601, 40717, 41059, 41431, 42551, 43079, 43163, 43303, 43453, 44081, 44399, 45163, 45611, 46111, 46223, 46391, 47219, 47989, 48047, 48241, 48577, 49097, 49703, 50293, 50501, 50507, 51661, 51773, 52187, 52343, 53029, 53843, 54301, 54671, 55003, 55403, 55423, 56107, 56321, 56741, 57971, 57979, 57995, 58493, 58811, 59537, 59977, 60553, 60881, 60911, 61709, 61921, 61969, 62537, 62669, 63053, 64193, 64759, 65279, 65501, 66001, 66113, 66991, 67031, 67051, 67091, 67549, 68333, 68933, 69103, 69781, 69965, 70103, 70129, 70471, 70703, 70813, 70817, 70897, 71009, 72587, 73207, 73687, 74233, 75197, 76211, 76477, 76613, 76763, 77593, 77807, 78709, 78851, 79021, 79267, 79511, 79957, 80753, 80939, 81167, 81211, 81413, 81581, 82409, 82441, 83651, 84289, 84593, 85307, 85637, 86003, 86159, 87949, 88865, 89291, 89495, 90101, 92123, 93173, 94411, 94891, 95449, 96071, 96077, 96101, 96121, 97313, 97939, 98239, 100051, 100633, 100691, 101593, 102271, 102961, 103139, 103937, 104143, 105313, 105593, 106039, 107117, 107249, 107407, 108091, 108121, 108341, 109117, 109399, 109801, 109957, 110131.

Some larger examples :