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cyclic n.  and  hex n.

First numbers that belong to both sets:

1, 7, 19, 37, 61, 91, 127, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1141, 1261, 1387, 1657, 1801, 1951, 2269, 2437, 2611, 2791, 2977, 3169, 3367, 3571, 3781, 3997, 4219, 4447, 4681, 4921, 5167, 5419, 5677, 5941, 6211, 6487, 7057, 7351, 7957, 8269, 8587, 8911, 9241, 9577, 9919, 10267, 10621, 10981, 11347, 11719, 12097, 12481, 12871, 13267, 13669, 14077, 14491, 14911, 15769, 16207, 16651, 17557, 18019, 18487, 18961, 19441, 19927, 20419, 20917, 21421, 21931, 22447, 22969, 23497, 24031, 24571, 25117, 25669, 26227, 26791, 27361, 27937, 29107, 30301, 30907, 31519, 32137, 33391, 34027, 34669, 35317, 35971, 36631, 37297, 37969, 38647, 39331, 40021, 40717, 41419, 42127, 42841, 44287, 45019, 45757, 47251, 48007, 48769, 49537, 50311, 51091, 51877, 52669, 53467, 54271, 55081, 55897, 56719, 57547, 58381, 59221, 60067, 60919, 61777, 62641, 65269, 66157, 67051, 68857, 69769, 70687, 71611, 73477, 74419, 75367, 76321, 77281, 79219, 80197, 81181, 82171, 84169, 85177, 87211, 88237, 89269, 91351, 92401, 94519, 95587, 96661, 97741, 98827, 99919, 101017, 102121, 103231, 104347, 105469, 106597, 107731, 108871, 110017, 111169, 112327, 113491, 114661, 115837, 117019, 118207, 119401, 120601, 121807, 123019, 124237, 125461, 126691, 127927, 129169, 130417, 131671, 132931, 135469, 138031, 139321, 140617, 141919, 144541, 145861, 147187, 149857, 151201, 152551, 153907, 155269, 156637, 158011, 159391, 160777, 162169, 163567, 164971, 166381, 167797, 169219, 170647, 172081, 173521, 176419, 179341, 180811, 183769, 185257, 186751, 188251, 189757, 191269, 192787, 194311, 195841, 197377, 198919, 200467, 202021, 205147, 209881, 211471, 213067, 216277, 217891, 219511, 222769, 224407, 227701, 229357, 231019, 232687, 234361, 236041, 237727, 239419, 241117, 242821, 244531, 246247, 247969, 249697, 251431, 253171, 254917, 256669, 258427, 260191, 263737, 265519, 267307, 269101, 270901, 272707, 274519, 276337, 278161, 279991, 281827, 283669, 285517, 289231, 291097, 292969, 294847, 296731, 298621, 302419.

Some larger examples :