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interprime n.  and  nialpdrome

First numbers that belong to both sets:

4, 6, 9, 21, 30, 42, 50, 60, 64, 72, 76, 81, 86, 93, 99, 111, 300, 420, 432, 441, 522, 532, 544, 552, 600, 610, 642, 650, 660, 730, 741, 754, 765, 771, 810, 822, 855, 861, 870, 882, 885, 933, 944, 950, 960, 974, 980, 987, 994, 1100, 2210, 3000, 3300, 3310, 3321, 3330, 4332, 4422, 4432, 4444, 5100, 5110, 5300, 5410, 5442, 5520, 5544, 6300, 6320, 6333, 6552, 6660, 7200, 7332, 7442, 7520, 7533, 7544, 7554, 7630, 7641, 7710, 7720, 7755, 7774, 8200, 8220, 8421, 8430, 8532, 8541, 8553, 8644, 8655, 8666, 8710, 8744, 8750, 8770, 8820, 8844, 8855, 8862, 8865, 8877, 9000, 9321, 9330, 9400, 9420, 9432, 9543, 9621, 9630, 9655, 9720, 9741, 9775, 9831, 9854, 9865, 9877, 9885, 9930, 9970, 9990, 22000, 22110, 22211, 30000, 33110, 33330, 42222, 43110, 43320, 44322, 44433, 52000, 54111, 54321, 54411, 54420, 54440, 55210, 55322, 55332, 55440, 55520, 55544, 61110, 62210, 63100, 64100, 64220, 64311, 64330, 65000, 65100, 65400, 65410, 65421, 65430, 65442, 65520, 65541, 65554, 66422, 66440, 66531, 72222, 74100, 74320, 74430, 75210, 75220, 75333, 75530, 75540, 75555, 76210, 76222, 76422, 76432, 76500, 76542, 76552, 76600, 76640, 76650, 77320, 77331, 77400, 77500, 77511, 77550, 77554, 77631, 77644, 77653, 77721, 77754, 81110, 82200, 82221, 83000, 83220, 84222, 84310, 84333, 84440, 85000, 85200, 85300, 85322, 85332, 85443, 85500, 85520, 85540, 86332, 86432, 86520, 86532, 86550, 86653, 87222, 87320, 87330, 87430, 87500, 87510, 87520, 87531, 87540, 87544, 87550, 87555, 87630, 87642, 87660, 87710, 87720, 87730, 87741, 88311, 88332, 88654, 88662, 88665, 88744, 88800, 88831, 88864, 88870, 91110, 92000, 92211, 92220, 93100, 93321, 93333, 94110, 94410, 94430, 94440, 94444, 95322, 95333, 95442, 95544, 95555, 96222, 96330, 96410, 96522, 96540, 96555, 96622, 96652, 96664.

Some larger examples :