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cyclic n.  and  star n.

First numbers that belong to both sets:

1, 13, 37, 73, 181, 337, 433, 541, 661, 793, 937, 1093, 1261, 1441, 1633, 1837, 2053, 2281, 2521, 2773, 3037, 3313, 3601, 3901, 4213, 4537, 4873, 5221, 5581, 5953, 6337, 6733, 7141, 7561, 7993, 8437, 8893, 9841, 10333, 10837, 11353, 12421, 12973, 13537, 14113, 14701, 15301, 15913, 16537, 17173, 17821, 18481, 19153, 19837, 20533, 21241, 21961, 22693, 23437, 24193, 24961, 25741, 27337, 28153, 28981, 29821, 30673, 31537, 32413, 33301, 34201, 35113, 36037, 36973, 37921, 38881, 39853, 40837, 41833, 42841, 43861, 44893, 45937, 46993, 48061, 49141, 50233, 51337, 52453, 53581, 54721, 55873, 57037, 59401, 60601, 61813, 64273, 65521, 66781, 68053, 69337, 70633, 71941, 73261, 74593, 75937, 77293, 82837, 84253, 85681, 87121, 88573, 90037, 91513, 93001, 96013, 99073, 100621, 102181, 103753, 105337, 106933, 108541, 110161, 111793, 113437, 115093, 116761, 118441, 120133, 121837, 123553, 125281, 127021, 128773, 130537, 132313, 134101, 135901, 137713, 139537, 141373, 143221, 145081, 146953, 150733, 152641, 154561, 156493, 158437, 162361, 164341, 166333, 168337, 170353, 172381, 176473, 178537, 180613, 182701, 184801, 186913, 189037, 191173, 193321, 195481, 197653, 199837, 202033, 204241, 206461, 208693, 210937, 213193, 215461, 217741, 220033, 222337, 224653, 229321, 231673, 234037, 236413, 238801, 241201, 243613, 246037, 248473, 250921, 253381, 255853, 258337, 260833, 263341, 265861, 268393, 270937, 276061, 278641, 281233, 283837, 286453, 289081, 291721, 294373, 299713, 302401, 305101, 307813, 310537, 313273, 316021, 318781, 321553, 324337, 327133, 329941, 335593, 341293, 344161, 347041, 349933, 352837, 355753, 358681, 361621, 367537, 370513, 373501, 376501, 379513, 382537, 385573, 388621, 391681, 394753, 397837, 400933, 407161, 410293, 413437, 416593, 419761, 422941, 426133, 429337, 432553, 435781, 439021, 445537, 448813, 452101, 455401, 458713, 462037, 465373, 468721, 472081, 475453, 478837, 482233, 485641, 489061, 492493, 495937, 499393, 502861, 506341, 509833, 516853, 520381, 523921, 527473, 531037, 534613, 538201, 541801, 545413, 549037, 552673.

Some larger examples :