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palindromic n.  and  wasteful n.

First numbers that belong to both sets:

4, 6, 8, 9, 22, 33, 44, 55, 66, 77, 88, 99, 171, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 323, 333, 363, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616, 626, 636, 646, 656, 666, 676, 696, 707, 717, 737, 747, 767, 777, 808, 818, 828, 838, 848, 858, 868, 878, 888, 898, 909, 939, 949, 959, 969, 979, 989, 999, 1001, 1111, 1221, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443, 3553, 3663, 3883, 4004, 4114, 4224, 4334, 4444, 4554, 4664, 4774, 4884, 4994, 5005, 5115, 5225, 5335, 5445, 5555, 5665, 5775, 5885, 5995, 6006, 6116, 6226, 6336, 6446, 6556, 6666, 6776, 6886, 6996, 7007, 7117, 7227, 7337, 7447, 7557, 7667, 7777, 7887, 7997, 8008, 8118, 8228, 8338, 8448, 8558, 8668, 8778, 8888, 8998, 9009, 9119, 9229, 9339, 9449, 9559, 9669, 9779, 9889, 9999, 10101, 10701, 11011, 11211, 11511, 11811, 12121, 12221, 13131, 13231, 13431, 13731, 14241, 14541, 14841, 15051, 15151, 15251, 15351, 15651, 15851, 15951, 16261, 16461, 16761, 16861, 17171, 17271, 17771, 17871, 18081, 18281, 18381, 18581, 18681, 18981, 19091, 19291, 19591, 20002, 20102, 20202, 20302, 20502, 20602, 20702, 20802, 20902, 21012, 21112, 21212, 21312, 21412, 21512, 21612, 21712, 21812, 21912, 22022, 22122, 22222, 22322, 22422, 22522, 22622, 22722, 22822, 22922, 23032, 23132, 23232, 23332, 23432, 23532, 23632, 23732, 23832, 23932, 24042, 24142, 24242, 24342, 24442, 24542, 24642, 24742, 24842, 24942, 25052, 25152, 25252, 25352, 25452, 25552, 25652, 25752, 25852, 26062, 26162, 26262, 26362, 26462, 26562, 26662, 26762, 26862, 26962, 27072, 27172, 27272, 27372, 27472, 27572.

Some larger examples :