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nude n.  and  palindromic n.

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 212, 222, 333, 424, 444, 515, 555, 636, 666, 777, 848, 888, 999, 1111, 1771, 2112, 2222, 2772, 3333, 4224, 4444, 5115, 5555, 5775, 6336, 6666, 7777, 8448, 8888, 9999, 11111, 11711, 13131, 17171, 21112, 21212, 21312, 21412, 21612, 22122, 22222, 22722, 23232, 23832, 26262, 27272, 27972, 31113, 33333, 39393, 42124, 42224, 42324, 42424, 42624, 42824, 44144, 44244, 44444, 44744, 46164, 46464, 48184, 48384, 51115, 51315, 51515, 53535, 55155, 55555, 55755, 57575, 61116, 61416, 62226, 63336, 63636, 63936, 66366, 66666, 69696, 77777, 82128, 84248, 84448, 84648, 84848, 88288, 88488, 88888, 93339, 99999, 111111, 171171, 211112, 212212, 213312, 214412, 216612, 221122, 222222, 231132, 234432, 261162, 272272, 279972, 333333, 421124, 422224, 423324, 424424, 426624, 428824, 441144, 442244, 444444, 462264, 468864, 481184, 483384, 511115, 513315, 515515, 531135, 551155, 555555, 575575, 612216, 618816, 621126, 633336, 636636, 639936, 663366, 666666, 693396, 717717, 777777, 821128, 842248, 844448, 846648, 848848, 861168, 882288, 884488, 888888, 999999, 1111111, 1113111, 1173711, 1331331, 1391931, 1711171, 1931391, 2111112, 2112112, 2114112, 2118112, 2121212, 2122212, 2124212, 2133312, 2136312, 2141412, 2142412, 2144412, 2163612, 2166612, 2169612, 2193912, 2211122, 2212122, 2221222, 2222222, 2223222, 2226222, 2231322, 2261622, 2267622, 2291922, 2313132, 2316132, 2321232, 2324232, 2332332, 2343432, 2346432, 2349432, 2362632, 2368632, 2381832, 2384832, 2613162, 2616162, 2619162, 2621262, 2632362, 2662662, 2673762, 2692962, 2722272, 2747472, 2774772, 2799972, 2913192, 2921292, 2938392, 2946492, 2962692, 3131313, 3191913, 3311133, 3333333, 3339333, 3911193, 3993993, 4211124, 4212124, 4214124, 4221224, 4222224, 4224224, 4228224, 4233324, 4236324, 4239324, 4241424, 4242424, 4244424, 4248424, 4263624, 4266624, 4281824, 4282824, 4284824, 4288824, 4296924, 4411144, 4412144, 4413144, 4414144, 4416144, 4418144, 4419144, 4421244, 4422244, 4424244, 4432344, 4438344, 4441444, 4442444, 4443444, 4444444, 4446444, 4462644, 4492944, 4612164, 4623264, 4626264, 4631364.

Some larger examples :