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amenable n.  and  palindromic n.

First numbers that belong to both sets:

1, 5, 8, 9, 33, 44, 77, 88, 101, 121, 141, 161, 181, 212, 232, 252, 272, 292, 313, 333, 353, 373, 393, 404, 424, 444, 464, 484, 505, 525, 545, 565, 585, 616, 636, 656, 676, 696, 717, 737, 757, 777, 797, 808, 828, 848, 868, 888, 909, 929, 949, 969, 989, 1001, 1221, 1441, 1661, 1881, 2112, 2332, 2552, 2772, 2992, 3113, 3333, 3553, 3773, 3993, 4004, 4224, 4444, 4664, 4884, 5005, 5225, 5445, 5665, 5885, 6116, 6336, 6556, 6776, 6996, 7117, 7337, 7557, 7777, 7997, 8008, 8228, 8448, 8668, 8888, 9009, 9229, 9449, 9669, 9889, 10001, 10101, 10201, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 12021, 12121, 12221, 12321, 12421, 12521, 12621, 12721, 12821, 12921, 14041, 14141, 14241, 14341, 14441, 14541, 14641, 14741, 14841, 14941, 16061, 16161, 16261, 16361, 16461, 16561, 16661, 16761, 16861, 16961, 18081, 18181, 18281, 18381, 18481, 18581, 18681, 18781, 18881, 18981, 21012, 21112, 21212, 21312, 21412, 21512, 21612, 21712, 21812, 21912, 23032, 23132, 23232, 23332, 23432, 23532, 23632, 23732, 23832, 23932, 25052, 25152, 25252, 25352, 25452, 25552, 25652, 25752, 25852, 25952, 27072, 27172, 27272, 27372, 27472, 27572, 27672, 27772, 27872, 27972, 29092, 29192, 29292, 29392, 29492, 29592, 29692, 29792, 29892, 29992, 31013, 31113, 31213, 31313, 31413, 31513, 31613, 31713, 31813, 31913, 33033, 33133, 33233, 33333, 33433, 33533, 33633, 33733, 33833, 33933, 35053, 35153, 35253, 35353, 35453, 35553, 35653, 35753, 35853, 35953, 37073, 37173, 37273, 37373, 37473, 37573, 37673, 37773, 37873, 37973, 39093, 39193, 39293, 39393, 39493, 39593, 39693, 39793, 39893, 39993, 40004, 40104, 40204, 40304, 40404, 40504, 40604, 40704, 40804, 40904, 42024, 42124, 42224, 42324, 42424, 42524, 42624, 42724, 42824, 42924, 44044, 44144, 44244, 44344, 44444, 44544, 44644, 44744, 44844, 44944, 46064, 46164.

Some larger examples :