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alternating n.  and  untouchable n.

First numbers that belong to both sets:

2, 5, 52, 96, 210, 216, 238, 276, 290, 292, 430, 472, 474, 498, 612, 658, 670, 818, 836, 852, 872, 892, 894, 896, 898, 1074, 1078, 1212, 1236, 1254, 1256, 1258, 1272, 1296, 1418, 1438, 1476, 1632, 1650, 1692, 1816, 1830, 1838, 1852, 1894, 1896, 3018, 3036, 3072, 3076, 3078, 3234, 3236, 3238, 3270, 3276, 3278, 3292, 3296, 3412, 3430, 3432, 3454, 3476, 3630, 3636, 3650, 3652, 3656, 3670, 3812, 3816, 3818, 3832, 3872, 3876, 5016, 5030, 5032, 5034, 5070, 5072, 5092, 5094, 5096, 5214, 5218, 5250, 5252, 5256, 5270, 5278, 5292, 5430, 5456, 5458, 5470, 5490, 5492, 5610, 5614, 5616, 5636, 5832, 5876, 5878, 5896, 7010, 7012, 7018, 7032, 7050, 7054, 7056, 7074, 7092, 7272, 7292, 7410, 7416, 7432, 7470, 7476, 7612, 7614, 7616, 7632, 7658, 7696, 7810, 7850, 7852, 7890, 7892, 9072, 9074, 9098, 9216, 9218, 9234, 9236, 9238, 9292, 9298, 9412, 9430, 9450, 9452, 9490, 9610, 9638, 9856, 9876, 9894, 9896, 9898, 21036, 21038, 21052, 21054, 21056, 21058, 21072, 21076, 21216, 21218, 21232, 21256, 21292, 21296, 21298, 21416, 21432, 21452, 21456, 21458, 21476, 21630, 21636, 21656, 21670, 21672, 21692, 21698, 21810, 21812, 21816, 21830, 21836, 21876, 21878, 21892, 23016, 23034, 23038, 23078, 23092, 23214, 23216, 23218, 23232, 23250, 23410, 23412, 23430, 23436, 23472, 23490, 23492, 23618, 23658, 23676, 23696, 23698, 23810, 23812, 23850, 23878, 23892, 23898, 25030, 25056, 25072, 25212, 25252, 25258, 25270, 25272, 25290, 25298, 25416, 25418, 25430, 25436, 25476, 25478, 25492, 25498, 25614, 25632, 25652, 25654, 25672, 25698, 25810, 25812, 25816, 25830, 25854, 25856, 25872, 25878, 25896, 25898, 27016, 27030, 27036, 27038, 27058, 27072, 27216, 27232, 27236, 27252, 27292, 27298, 27416, 27472, 27474, 27492, 27636, 27638, 27672, 27696, 27816, 27858, 27872, 27876, 27878, 27892.

Some larger examples :