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equidigital n.  and  interprime n.

First numbers that belong to both sets:

15, 21, 64, 81, 105, 111, 129, 134, 160, 192, 205, 217, 405, 1003, 1011, 1095, 1106, 1113, 1120, 1126, 1152, 1167, 1184, 1207, 1226, 1234, 1281, 1286, 1294, 1299, 1344, 1377, 1431, 1465, 1491, 1505, 1517, 1527, 1537, 1546, 1563, 1569, 1647, 1728, 1750, 1795, 1817, 1839, 1869, 1895, 1922, 1941, 1983, 2058, 2075, 2105, 2157, 2191, 2217, 2229, 2241, 2271, 2303, 2336, 2349, 2391, 2430, 2463, 2592, 2619, 2627, 2661, 2688, 2811, 2835, 2859, 2883, 2913, 2933, 3073, 3265, 3321, 3337, 3353, 3505, 3665, 3750, 3840, 4105, 4131, 4189, 4293, 4394, 4415, 4535, 4555, 4685, 5184, 5913, 6656, 7168, 7209, 7290, 7442, 7533, 8750, 10085, 10096, 10155, 10173, 10187, 10202, 10217, 10233, 10245, 10250, 10256, 10295, 10363, 10493, 10507, 10563, 10599, 10635, 10645, 10654, 10665, 10677, 10689, 10717, 10731, 10762, 10785, 10834, 10864, 10875, 10886, 10897, 10983, 11015, 11085, 11103, 11205, 11259, 11267, 11283, 11293, 11314, 11319, 11361, 11405, 11417, 11469, 11477, 11486, 11494, 11595, 11607, 11667, 11725, 11737, 11786, 11795, 11824, 11829, 11851, 11906, 11936, 11947, 12009, 12039, 12085, 12131, 12146, 12153, 12219, 12233, 12266, 12273, 12279, 12295, 12326, 12345, 12385, 12405, 12417, 12427, 12435, 12494, 12514, 12533, 12561, 12693, 12717, 12795, 12847, 12871, 12891, 12921, 12976, 12981, 12992, 13021, 13056, 13106, 13115, 13149, 13155, 13174, 13235, 13245, 13254, 13263, 13279, 13303, 13353, 13389, 13405, 13419, 13446, 13454, 13466, 13473, 13594, 13605, 13641, 13689, 13703, 13726, 13785, 13875, 13881, 13917, 13982, 14054, 14125, 14151, 14175, 14187, 14395, 14415, 14455, 14511, 14592, 14607, 14624, 14631, 14655, 14691, 14720, 14727, 14750, 14769, 14829, 14837, 14889, 14954, 14998, 15155, 15167, 15250, 15261, 15303, 15360, 15375, 15407, 15441, 15519, 15575, 15635, 15681, 15744, 15841, 15879, 15904, 16045, 16119, 16162, 16205, 16251.

Some larger examples :