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magic constant  and  odious n.

First numbers that belong to both sets:

1, 369, 505, 671, 2465, 3439, 7825, 8801, 10990, 12209, 17985, 25345, 27455, 34481, 39775, 42614, 51935, 58849, 74465, 87836, 92625, 113521, 137345, 157250, 194545, 219526, 246559, 329295, 340780, 352529, 364545, 376831, 415339, 456385, 485199, 500050, 546415, 578865, 595561, 647569, 665555, 702520, 721505, 740829, 760495, 821575, 842639, 930495, 976625, 1073409, 1203119, 1314105, 1372070, 1431715, 1524385, 1556141, 1620970, 1687575, 1721551, 1755980, 1790865, 1826209, 1935025, 1972235, 2009919, 2086721, 2125845, 2205554, 2370900, 2413489, 2725976, 2772705, 2819965, 2916090, 2964961, 3014375, 3064335, 3114844, 3217521, 3269695, 3594625, 3707535, 4060401, 4244934, 4307665, 4371011, 4831905, 4900279, 5544895, 5619824, 5695425, 6004609, 6083615, 6243700, 6324785, 6489055, 6656145, 6740755, 6826079, 7263514, 7443591, 7626620, 7906751, 8097265, 8487425, 9095855, 9304945, 9410681, 9841635, 9951391, 10173345, 10285549, 10627105, 10742615, 11094161, 11213025, 12577025, 12836335, 12967316, 13231945, 13771955, 13909215, 14047384, 14326461, 14467375, 15332305, 15479729, 16078875, 17643940, 18132511, 18463185, 18797855, 18966696, 19136545, 19307405, 19479279, 19826081, 20001015, 20176975, 20353964, 20531985, 20711041, 21254449, 21807280, 23328180, 23523121, 23719145, 24514131, 24918200, 25532591, 26367375, 26578876, 27220159, 27653361, 28533505, 29432129, 30349425, 31285585, 31522595, 32240801, 32725615, 33461911, 33709775, 33958860, 34209169, 35736895, 36517525, 36780239, 37309441, 38383025, 39201590, 39477009, 39753715, 40873469, 41441146, 41726945, 42014055, 42302479, 42592220, 43469375, 44060785, 44358491, 44657535, 44957920, 45867151, 47098415, 48986321, 49626655, 49948904, 50597581, 50924015, 51581089, 52243791, 54607915, 55990325, 56690194, 57395871, 58465329, 60643935, 61012216, 61381985, 63253255, 65162175, 65936369, 67503105, 69899439, 70304260, 70710641, 71528095, 73181855, 74018209, 74860911, 75709985, 76136919, 76565455, 77427345, 77860705, 79610315, 80051775, 82283570, 84098580, 85016009, 85940086, 87338719, 88279521, 89227055, 90181345, 95054975, 96050305, 98061761, 99077935, 99588644, 100101105, 101649030, 102689795, 103737640, 104264225, 105322735, 105854666, 106388385, 107461199, 109628415, 111272811, 111824575, 112378160, 112933569, 113490805, 114610770, 115173505, 119741841, 120321235, 120902495, 122070625, 123836890, 124429409, 125023815, 125620111, 126818385, 128024255, 128630046, 129237745, 131687681, 132304965, 132924175, 134168385, 134793391, 135420335, 136680049, 137947551, 138584230, 139222865, 140506015, 141150536, 141797025, 143095919, 143748330, 145717455, 147040145, 147704481, 149039150.

Some larger examples :