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interprime n.  and  lucky n.

First numbers that belong to both sets:

9, 15, 21, 69, 93, 99, 105, 111, 129, 195, 205, 231, 393, 399, 483, 489, 495, 615, 645, 723, 741, 855, 885, 897, 933, 1011, 1095, 1167, 1197, 1281, 1485, 1491, 1563, 1575, 1599, 1611, 1737, 1827, 1839, 1869, 1941, 1983, 1995, 2001, 2085, 2121, 2217, 2271, 2277, 2379, 2439, 2661, 2667, 2835, 2913, 3039, 3055, 3073, 3099, 3175, 3213, 3381, 3453, 3465, 3495, 3565, 3675, 3795, 3849, 3879, 3909, 4105, 4131, 4189, 4521, 4587, 4629, 5001, 5169, 5229, 5235, 5577, 5649, 5655, 5691, 5817, 5833, 5889, 5913, 5967, 5997, 6009, 6147, 6471, 6477, 6667, 6849, 6891, 6909, 6999, 7041, 7233, 7245, 7341, 7503, 7533, 7567, 7575, 7677, 7689, 7701, 7755, 7791, 7881, 8001, 8169, 8175, 8253, 8289, 8421, 8445, 8553, 8577, 8589, 8635, 8655, 8673, 8757, 8793, 8805, 8931, 8937, 9009, 9063, 9135, 9177, 9249, 9267, 9315, 9339, 9543, 9549, 9621, 9727, 9775, 9789, 9807, 9915, 10173, 10317, 10363, 10431, 10443, 10461, 10507, 10563, 10599, 10635, 10731, 10785, 10923, 10953, 10965, 11077, 11205, 11247, 11259, 11283, 11583, 11667, 11679, 11725, 11781, 11865, 11877, 12159, 12207, 12285, 12295, 12411, 12417, 12427, 12435, 12741, 12903, 13021, 13167, 13245, 13279, 13419, 13473, 13695, 13803, 14031, 14287, 14395, 14427, 14607, 14691, 14715, 14775, 14817, 14883, 14943, 15057, 15237, 15261, 15519, 15645, 15655, 15675, 15735, 15879, 16045, 16191, 16287, 16449, 16479, 16557, 16701, 16953, 16971, 17085, 17103, 17355, 17391, 17409, 17545, 17589, 17625, 17695, 17733, 17965, 18001, 18175, 18195, 18295, 18375, 18399, 18441, 18459, 18765, 18849, 18915, 19195, 19225, 19263, 19389, 19807, 20067, 20355, 20379, 20403, 20605, 20953, 21015, 21021, 21027, 21153, 21189, 21315, 21381, 21615, 21655, 21819, 21867, 21933, 22155, 22165, 22281, 22305, 22437, 22461, 22521, 22569, 22629, 23007, 23061, 23067, 23137.

Some larger examples :