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amenable n.  and  hoax n.

First numbers that belong to both sets:

84, 85, 136, 160, 265, 308, 336, 361, 364, 424, 456, 476, 516, 517, 644, 645, 660, 732, 860, 861, 913, 948, 985, 1116, 1148, 1165, 1312, 1344, 1404, 1484, 1576, 1581, 1600, 1612, 1633, 1665, 1708, 1752, 1812, 1824, 1876, 1921, 1924, 2008, 2064, 2173, 2232, 2236, 2265, 2325, 2352, 2356, 2373, 2401, 2409, 2461, 2500, 2541, 2565, 2605, 2616, 2625, 2640, 2760, 2785, 2872, 2924, 2960, 2965, 3036, 3048, 3164, 3172, 3268, 3285, 3344, 3345, 3381, 3393, 3476, 3484, 3505, 3552, 3556, 3592, 3625, 3649, 3712, 3736, 3792, 3836, 3865, 3892, 3912, 3920, 3933, 3973, 4024, 4116, 4148, 4160, 4173, 4188, 4189, 4209, 4212, 4228, 4268, 4344, 4369, 4396, 4456, 4460, 4473, 4564, 4636, 4656, 4676, 4744, 4765, 4776, 4820, 4824, 4844, 4905, 4920, 4980, 4981, 5052, 5068, 5145, 5168, 5176, 5253, 5268, 5269, 5305, 5332, 5344, 5348, 5397, 5412, 5425, 5464, 5484, 5485, 5525, 5548, 5612, 5652, 5752, 5840, 6016, 6060, 6184, 6244, 6260, 6356, 6364, 6385, 6457, 6472, 6500, 6504, 6512, 6524, 6564, 6585, 6596, 6600, 6604, 6616, 6620, 6633, 6692, 6693, 6741, 6900, 6904, 6960, 6980, 6981, 7008, 7028, 7048, 7052, 7076, 7089, 7196, 7212, 7228, 7236, 7249, 7268, 7364, 7428, 7465, 7525, 7624, 7756, 7809, 7924, 8005, 8076, 8077, 8084, 8145, 8149, 8164, 8185, 8224, 8244, 8257, 8277, 8284, 8292, 8308, 8325, 8420, 8421, 8508, 8545, 8600, 8653, 8673, 8720, 8724, 8780, 8816, 8924, 8932, 9028, 9052, 9096, 9116, 9180, 9193, 9229, 9285, 9301, 9333, 9412, 9425, 9436, 9528, 9540, 9652, 9716, 9717, 9772, 9861, 9916, 9940, 9985, 10044, 10188, 10192, 10240, 10268, 10392, 10464, 10489, 10492, 10560, 10604, 10624, 10669, 10689, 10704, 10705, 10761, 10780, 10797, 10884, 10936, 10948, 11065, 11124, 11209, 11228.

Some larger examples :