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Duffinian n.  and  palindromic n.

First numbers that belong to both sets:

4, 8, 9, 55, 77, 111, 121, 161, 171, 242, 323, 333, 343, 363, 484, 505, 515, 525, 535, 565, 575, 595, 676, 707, 737, 767, 777, 939, 949, 959, 979, 989, 999, 1111, 1331, 1661, 1771, 1991, 3113, 3223, 3443, 3553, 3773, 3883, 5335, 5555, 5665, 5885, 7117, 7337, 7447, 7667, 7777, 7997, 9119, 9229, 9449, 9559, 9779, 9889, 10001, 10201, 10801, 10901, 11111, 11511, 11611, 11711, 11811, 11911, 12121, 12221, 12521, 13031, 13131, 13231, 13431, 13531, 13631, 14041, 14141, 14441, 14641, 14941, 15151, 15251, 15751, 15951, 16261, 16761, 16861, 16961, 17071, 17371, 17571, 17671, 17771, 18281, 18581, 18781, 18881, 19091, 19191, 19291, 19591, 19791, 20402, 30503, 30603, 31113, 31313, 31413, 31613, 31813, 32023, 32723, 32923, 33133, 33233, 33433, 33733, 33933, 34043, 34243, 34343, 34643, 34743, 34943, 35453, 35653, 35953, 36163, 36463, 36763, 36863, 37073, 37173, 37373, 37673, 37773, 37873, 37973, 38383, 38483, 38583, 38683, 38883, 38983, 39193, 39393, 39493, 39593, 39793, 40804, 44944, 50005, 50105, 50305, 50405, 50705, 50905, 51115, 51215, 51515, 51715, 51815, 52025, 52525, 52625, 52825, 53035, 53135, 53335, 53435, 53635, 53735, 53935, 55355, 55555, 55655, 55855, 55955, 56065, 56365, 56465, 56765, 56965, 57175, 57575, 57775, 57875, 58085, 58285, 58385, 58585, 58685, 58885, 58985, 59095, 59395, 59495, 59995, 69696, 70007, 70307, 70807, 70907, 71017, 71117, 71417, 71517, 71717, 72127, 72327, 72427, 72827, 73137, 73337, 73537, 73737, 73837, 73937, 74147, 74447, 74647, 74847, 74947, 75157, 75357, 75457, 75657, 75757, 75857, 76067, 76267, 76567, 76967, 77177, 77277, 77677, 78087, 78187, 78287, 78587, 78687, 79097, 79297, 79497, 79797, 79897, 90109, 90209, 90309, 90409, 90509, 90809, 91219, 91319, 91519, 91619, 91719, 91919, 92029, 92129, 92329, 92429, 92629, 92929, 93339, 93439, 93539, 93839, 94249, 94449, 95059, 95159, 95359, 95659, 95759, 95859.

Some larger examples :