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Duffinian n.  and  upside-down n.

First numbers that belong to both sets:

55, 64, 1379, 1469, 1649, 1739, 1829, 1919, 2738, 3197, 3287, 3647, 3737, 3827, 5285, 5375, 5465, 5555, 5735, 5825, 5915, 7373, 7463, 7913, 8192, 9641, 9731, 9821, 9911, 11599, 13579, 14569, 16549, 18529, 19519, 31597, 34567, 35557, 36547, 38527, 39517, 51595, 53575, 55555, 56545, 57535, 58525, 59515, 72583, 73573, 74563, 77533, 78523, 93571, 95551, 96541, 97531, 98521, 99511, 111999, 112899, 113799, 116499, 117399, 119199, 121989, 123789, 125589, 127389, 129189, 132879, 133779, 134679, 135579, 138279, 141969, 142869, 144669, 145569, 146469, 147369, 149169, 151959, 154659, 155559, 156459, 157359, 161949, 162849, 163749, 165549, 169149, 171939, 176439, 177339, 179139, 182829, 184629, 185529, 186429, 188229, 193719, 195519, 198219, 199119, 314697, 315597, 316497, 317397, 319197, 322887, 323787, 325587, 327387, 333777, 334677, 337377, 338277, 341967, 344667, 345567, 348267, 351957, 352857, 353757, 354657, 356457, 358257, 359157, 362847, 366447, 367347, 369147, 371937, 372837, 375537, 377337, 378237, 382827, 383727, 385527, 389127, 391917, 393717, 394617, 395517, 396417, 397317, 398217, 399117, 535575, 538275, 583725, 585525, 586425, 711993, 712893, 713793, 715593, 716493, 718293, 719193, 723783, 724683, 725583, 726483, 727383, 732873, 733773, 734673, 736473, 738273, 739173, 741963, 746463, 748263, 749163, 752853, 755553, 756453, 757353, 762843, 763743, 765543, 767343, 768243, 771933, 772833, 773733, 774633, 778233, 779133, 782823, 783723, 784623, 788223, 791913, 794613, 795513, 796413, 798213, 799113, 911991, 913791, 914691, 915591, 916491, 922881, 925581, 926481, 932871, 934671, 936471, 938271, 939171, 941961, 944661, 945561, 946461, 947361, 948261, 952851, 956451, 957351, 958251, 959151, 961941, 963741, 964641, 965541, 966441, 968241, 971931, 972831, 974631, 976431, 977331, 979131, 981921, 983721, 985521, 988221, 991911, 992811, 993711, 994611, 997311, 998211, 999111, 1115999, 1135799, 1145699, 1155599, 1165499, 1175399, 1195199, 1215989, 1225889, 1255589, 1265489, 1275389, 1295189, 1325879, 1335779, 1345679, 1365479, 1385279, 1415969, 1425869, 1435769, 1475369, 1495169, 1515959, 1535759, 1545659, 1555559, 1565459, 1575359, 1585259, 1595159.

Some larger examples :