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interprime n.  and  repunit

First numbers that belong to both sets:

15, 21, 111, 381, 2955, 3081, 3423, 4971, 5403, 7240, 7381, 8373, 8421, 8931, 10101, 10507, 14763, 17031, 23871, 25761, 39403, 40603, 43057, 48621, 49063, 61257, 67341, 69905, 71557, 87165, 90301, 98283, 107913, 112945, 120100, 132861, 135793, 168421, 168511, 169333, 178507, 190533, 196693, 216691, 226101, 230764, 235711, 238633, 242235, 249501, 262143, 267807, 303051, 306363, 347511, 352243, 361803, 365421, 376383, 410241, 429681, 430993, 440233, 442891, 474033, 546861, 554281, 587523, 592131, 653673, 683103, 696391, 701407, 750823, 754293, 759513, 796557, 856551, 863971, 869557, 1001001, 1025157, 1035307, 1037343, 1049601, 1063993, 1107757, 1118481, 1163163, 1189191, 1228773, 1262253, 1282557, 1343211, 1367731, 1412533, 1460473, 1472583, 1499401, 1536361, 1556257, 1609093, 1634563, 1639681, 1652511, 1655083, 1680913, 1714791, 1746363, 1775557, 1826553, 1927933, 1930711, 1953007, 1978243, 2218611, 2265384, 2314963, 2385481, 2407153, 2419581, 2485353, 2494821, 2504307, 2523333, 2574421, 2590260, 2613660, 2668323, 2763907, 2787231, 2814007, 2820721, 2830807, 2970453, 2973901, 3011961, 3170181, 3216643, 3317863, 3365391, 3420651, 3521253, 3570211, 3669141, 3680643, 3726831, 3847483, 3894700, 4030057, 4054183, 4171807, 4245661, 4291113, 4340973, 4454211, 4458433, 4488043, 4496521, 4685061, 4685520, 4719757, 4881891, 4904011, 4948401, 4970671, 5096307, 5164257, 5246391, 5315331, 5324557, 5347657, 5421913, 5440557, 5743213, 5796057, 5844307, 6014757, 6063907, 6133053, 6207573, 6297591, 6403431, 6418623, 6586923, 6617757, 6757401, 6877507, 6914271, 7088907, 7201173, 7281903, 7384807, 7625883, 7675671, 7759011, 7927041, 8040061, 8171023, 8176741, 8199633, 8283415, 8354991, 8372343, 8476833, 8705451, 8784459, 8794191, 8835757, 8841703, 9045057, 9173220, 9189993, 9336081, 9354423, 9415693, 9464853, 9557373, 9875307, 10179291, 10313733, 10358743, 10507323, 10650433, 10702713, 10774807, 10801083, 11039007, 11058951, 11199063, 11272807, 11289825, 11319861, 11340057, 11468383, 11604243, 11926663, 11954307, 12211531, 12267507, 12379984, 12408007, 12422101, 12520983, 12606051, 12677161, 12848641, 12970803, 13035711, 13158757, 13200189, 13209591, 13428561, 13568173, 13619791, 13715913, 13782657, 13901713, 14088763, 14352733, 14390643, 14481831, 14965293, 15035007, 15058281, 15130480, 15245121, 15362481, 15440971, 15772813, 15820507, 15876504, 16148343, 16781313, 16855131, 17044513, 17501673, 17593831, 17602221, 17804181.

Some larger examples :