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happy n.  and  hoax n.

First numbers that belong to both sets:

94, 319, 391, 644, 860, 913, 1148, 1484, 1581, 1752, 1812, 1903, 2008, 2275, 2751, 3091, 3736, 3920, 4148, 4275, 4414, 4460, 4636, 4744, 4824, 4855, 5242, 5268, 5422, 5425, 5458, 5485, 5525, 5548, 5715, 5742, 5752, 5854, 6364, 6616, 6904, 7048, 7196, 7428, 7447, 7525, 8244, 8545, 8600, 8724, 9031, 9301, 9716, 10188, 11124, 11232, 11476, 12192, 12226, 12256, 12262, 12318, 12366, 12546, 12556, 12622, 12658, 12880, 12939, 12972, 13428, 13518, 13748, 13815, 14084, 14472, 14480, 14494, 14716, 14724, 15018, 15164, 15256, 15286, 15682, 15720, 15780, 15813, 15976, 16036, 16222, 16245, 16285, 16425, 16552, 16582, 16975, 17164, 17226, 17250, 17276, 17324, 17936, 18018, 18025, 18404, 18562, 19590, 19920, 20542, 20844, 21226, 21262, 21268, 21625, 21685, 21865, 22054, 22119, 22347, 22348, 22508, 22516, 22671, 22738, 22837, 22971, 23148, 23474, 23725, 24259, 24273, 24345, 24435, 24480, 24502, 24732, 25156, 25294, 25429, 25434, 25618, 25628, 25675, 25948, 26154, 26185, 26348, 26518, 26580, 27126, 27238, 27382, 27540, 27546, 27840, 28132, 28216, 28557, 28650, 29139, 29193, 29254, 29398, 29542, 29712, 29893, 29938, 30056, 30076, 30132, 30564, 30664, 30766, 30926, 31228, 31266, 31339, 32118, 32278, 32284, 32484, 32812, 32827, 32899, 32989, 32991, 33436, 33550, 33604, 33892, 34112, 34254, 34452, 34458, 34544, 34555, 34722, 34725, 34978, 34987, 35128, 35272, 35350, 35425, 35545, 36136, 36706, 36890, 36932, 37144, 37196, 37224, 37498, 37606, 37683, 37822, 37894, 38763, 38960, 39200, 39478, 39678, 39874, 39982, 40257, 40284, 40477, 40522, 40554, 40585, 40725, 40752, 40855, 40944, 41044, 41075, 41176, 41283, 41468, 41494, 41556, 41625, 41648, 41840, 41988, 42075, 42435, 42657, 42765, 42834, 43172, 43175, 43224, 43248, 43284, 43336, 43854, 43879, 44060, 44172, 44336, 44442, 44525, 44532, 44600, 45022, 45036, 45156, 45164, 45208, 45216, 45270, 45333, 45405, 45508, 45580, 45805, 45922, 45990.

Some larger examples :