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arithmetic n.  and  hoax n.

First numbers that belong to both sets:

22, 85, 94, 166, 265, 308, 319, 355, 361, 382, 391, 438, 454, 456, 476, 483, 517, 526, 535, 627, 644, 645, 654, 660, 663, 690, 702, 735, 762, 855, 860, 861, 895, 913, 915, 958, 985, 1086, 1111, 1148, 1165, 1219, 1255, 1484, 1507, 1550, 1581, 1626, 1633, 1650, 1665, 1678, 1795, 1822, 1824, 1842, 1894, 1903, 1921, 1966, 2038, 2067, 2155, 2166, 2173, 2182, 2227, 2232, 2265, 2326, 2373, 2409, 2461, 2515, 2565, 2605, 2614, 2625, 2679, 2751, 2760, 2785, 2839, 2872, 2902, 2911, 2924, 2958, 2965, 2974, 3036, 3046, 3048, 3091, 3138, 3164, 3246, 3285, 3339, 3344, 3345, 3381, 3390, 3393, 3476, 3505, 3552, 3595, 3615, 3618, 3622, 3625, 3630, 3649, 3694, 3792, 3836, 3850, 3865, 3912, 3930, 3933, 3973, 4024, 4054, 4126, 4148, 4160, 4173, 4189, 4191, 4198, 4209, 4235, 4268, 4279, 4369, 4414, 4460, 4473, 4590, 4676, 4702, 4765, 4776, 4794, 4820, 4844, 4855, 4905, 4918, 4974, 4980, 4981, 5062, 5071, 5094, 5145, 5150, 5168, 5176, 5253, 5269, 5298, 5305, 5344, 5348, 5397, 5412, 5422, 5485, 5525, 5539, 5612, 5638, 5642, 5715, 5742, 5752, 5854, 5874, 5926, 5935, 5946, 5998, 6016, 6027, 6054, 6060, 6115, 6187, 6259, 6260, 6295, 6315, 6356, 6385, 6390, 6439, 6457, 6500, 6502, 6504, 6524, 6531, 6567, 6583, 6585, 6596, 6600, 6603, 6620, 6633, 6692, 6693, 6702, 6718, 6741, 6835, 6855, 6904, 6934, 6950, 6960, 6980, 6981, 7008, 7026, 7028, 7038, 7051, 7052, 7062, 7076, 7078, 7089, 7150, 7195, 7196, 7249, 7268, 7287, 7335, 7339, 7364, 7438, 7447, 7465, 7503, 7506, 7627, 7674, 7683, 7726, 7782, 7809, 7915, 8005, 8014, 8023, 8077, 8084, 8091, 8095, 8145, 8149, 8158, 8185, 8214, 8257, 8277, 8334, 8347, 8415, 8420, 8421, 8466, 8518, 8545, 8653.

Some larger examples :