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interprime n.  and  plaindrome

First numbers that belong to both sets:

4, 6, 9, 12, 15, 18, 26, 34, 39, 45, 56, 69, 99, 111, 129, 134, 138, 144, 225, 228, 236, 246, 266, 279, 288, 334, 348, 356, 399, 446, 459, 489, 566, 667, 1113, 1126, 1158, 1167, 1226, 1234, 1268, 1278, 1299, 1344, 1377, 1449, 1456, 1488, 1556, 1569, 1599, 1668, 1788, 2229, 2238, 2247, 2259, 2268, 2277, 2336, 2344, 2349, 2379, 2444, 2568, 2667, 2688, 2799, 3337, 3345, 3366, 3399, 3459, 3468, 3558, 3588, 3699, 4444, 4449, 4488, 4555, 4668, 4788, 5566, 5577, 5889, 6667, 6999, 11115, 11118, 11125, 11166, 11226, 11247, 11259, 11267, 11388, 11445, 11457, 11469, 11477, 11667, 11679, 11778, 12233, 12246, 12258, 12266, 12279, 12336, 12345, 12378, 12444, 12489, 13334, 13338, 13389, 13446, 13466, 13689, 14448, 14455, 14559, 14577, 14889, 15555, 15669, 15789, 15888, 16667, 16799, 17799, 22238, 22278, 22346, 22358, 22368, 22444, 22558, 22569, 22889, 23336, 23348, 23466, 23559, 23666, 23688, 24456, 24477, 25569, 25578, 27888, 27999, 33337, 33345, 33348, 33356, 33368, 33459, 33555, 33566, 33579, 33588, 34448, 34477, 34566, 35556, 35799, 35888, 36789, 39999, 44468, 44499, 44556, 45555, 45578, 45588, 46689, 46789, 47778, 47999, 55677, 55899, 56667, 57777, 57789, 58899, 66668, 66699, 66777, 69999, 77778, 77799, 78888, 111114, 111124, 111135, 111146, 111168, 111189, 111222, 111228, 111258, 111266, 111339, 111344, 111455, 111477, 111489, 111558, 111579, 112239, 112244, 112248, 112257, 112334, 112338, 112344, 112355, 112444, 112689, 112779, 112889, 113335, 113349, 113358, 113367, 113445, 113478, 113499, 113579, 113778, 114459, 114666, 114777, 114789, 114999, 115557, 115566, 115599, 115779, 115788, 116688, 118899, 122225, 122257, 122289, 122337, 122355, 122388, 122446, 122499, 122559, 122588, 122678, 122889, 123357, 123378, 123388, 123399, 123444, 123468, 123567, 123588, 123689, 123789, 123899, 123999, 124589, 124779, 124788, 126668, 133389, 133449, 133466, 133577, 134457, 134589, 134679, 135666.

Some larger examples :