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congruent n.  and  palindromic n.

First numbers that belong to both sets:

5, 6, 7, 22, 55, 77, 88, 101, 111, 141, 151, 161, 181, 191, 212, 222, 252, 262, 303, 313, 323, 333, 343, 353, 373, 383, 404, 414, 434, 444, 454, 464, 494, 505, 525, 535, 565, 575, 585, 606, 616, 636, 646, 656, 686, 696, 717, 727, 757, 767, 777, 797, 828, 838, 848, 878, 888, 909, 919, 949, 959, 989, 999, 1111, 1221, 1551, 1661, 1991, 2222, 2332, 2552, 2662, 2772, 3003, 3223, 3333, 3443, 3663, 3773, 4114, 4334, 4444, 4664, 4774, 4884, 5005, 5115, 5335, 5445, 5775, 5885, 6006, 6446, 6556, 6776, 6886, 6996, 7007, 7117, 7447, 7557, 7887, 7997, 8118, 8558, 8668, 8888, 8998, 9119, 9229, 9339, 9559, 9669, 9779, 9999, 10001, 10101, 10301, 10501, 10601, 10701, 10901, 11111, 11211, 11311, 11511, 11711, 11811, 11911, 12021, 12121, 12221, 12421, 12621, 12821, 13031, 13231, 13431, 13531, 13631, 13831, 14141, 14341, 14541, 14741, 14841, 14941, 15151, 15351, 15551, 15751, 15951, 16061, 16261, 16461, 16661, 16761, 16861, 17071, 17271, 17471, 17671, 17871, 18081, 18181, 18381, 18581, 18781, 18981, 19191, 19391, 19591, 19791, 19991, 20002, 20102, 20302, 20502, 20702, 20902, 21012, 21112, 21212, 21312, 21712, 21812, 21912, 22022, 22222, 22422, 22622, 22822, 23032, 23132, 23632, 23732, 23832, 23932, 24142, 24342, 24542, 24742, 24942, 25052, 25552, 25652, 25752, 25852, 25952, 26062, 26262, 26462, 26662, 26862, 27072, 27472, 27572, 27672, 27772, 27872, 27972, 28182, 28282, 28382, 28582, 28782, 28982, 29192, 29392, 29492, 29592, 29692, 29792, 29892, 29992, 30103, 30303, 30503, 30703, 30903, 31013, 31213, 31413, 31613, 31813, 32023, 32223, 32423, 32623, 32823, 33133, 33333, 33533, 33733, 33933, 34143, 34343, 34543, 34743, 34943, 35053, 35253, 35353, 35453, 35653, 35853, 35953, 36063, 36263, 36463, 36663, 36863, 37173, 37373, 37573, 37773, 37873, 37973, 38183, 38383.

Some larger examples :