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congruent n.  and  hoax n.

First numbers that belong to both sets:

22, 84, 85, 94, 136, 166, 265, 308, 319, 336, 382, 391, 438, 454, 476, 517, 526, 535, 644, 645, 654, 660, 663, 702, 732, 735, 855, 860, 861, 895, 915, 948, 958, 985, 1086, 1111, 1116, 1148, 1165, 1255, 1282, 1344, 1404, 1484, 1550, 1581, 1633, 1678, 1752, 1812, 1822, 1858, 1876, 1894, 1903, 1966, 2008, 2038, 2166, 2173, 2182, 2232, 2236, 2325, 2326, 2356, 2373, 2434, 2461, 2541, 2565, 2605, 2614, 2616, 2640, 2679, 2751, 2839, 2872, 2902, 2911, 2924, 2958, 2965, 2974, 3036, 3046, 3164, 3172, 3246, 3285, 3339, 3381, 3390, 3474, 3476, 3484, 3552, 3556, 3595, 3615, 3622, 3625, 3630, 3694, 3736, 3792, 3836, 3850, 3865, 3892, 3920, 3930, 3933, 3973, 4024, 4054, 4116, 4126, 4148, 4160, 4173, 4188, 4189, 4191, 4198, 4212, 4228, 4279, 4344, 4414, 4564, 4590, 4636, 4656, 4676, 4702, 4744, 4765, 4794, 4820, 4824, 4855, 4918, 4920, 4974, 4980, 4981, 5022, 5052, 5062, 5071, 5094, 5150, 5168, 5176, 5253, 5268, 5269, 5332, 5344, 5397, 5422, 5464, 5485, 5525, 5548, 5602, 5638, 5652, 5742, 5752, 5840, 5854, 5926, 5935, 5998, 6016, 6054, 6066, 6175, 6244, 6260, 6295, 6356, 6364, 6390, 6439, 6500, 6502, 6512, 6524, 6531, 6567, 6583, 6596, 6604, 6616, 6620, 6693, 6702, 6718, 6741, 6855, 6900, 6904, 6934, 6950, 6980, 6981, 7008, 7028, 7038, 7048, 7062, 7078, 7150, 7196, 7228, 7287, 7335, 7438, 7447, 7503, 7525, 7650, 7726, 7756, 7782, 7924, 8005, 8014, 8023, 8077, 8084, 8095, 8145, 8149, 8158, 8214, 8224, 8244, 8277, 8284, 8308, 8325, 8334, 8415, 8421, 8508, 8518, 8600, 8653, 8724, 8780, 8790, 8816, 8924, 8955, 8982, 9015, 9028, 9031, 9052, 9094, 9116, 9166, 9180, 9229, 9285, 9294, 9301, 9333, 9350, 9382, 9436, 9483, 9528, 9535, 9540.

Some larger examples :