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alternating n.  and  brilliant n.

First numbers that belong to both sets:

4, 6, 9, 10, 14, 21, 25, 49, 121, 143, 169, 187, 323, 341, 361, 527, 529, 583, 589, 703, 767, 781, 901, 923, 943, 949, 961, 989, 2183, 2501, 2581, 2701, 2747, 2923, 4183, 4187, 4189, 4307, 12769, 16129, 16789, 18769, 18923, 30301, 30523, 30929, 30967, 32387, 32743, 32761, 34121, 34163, 34189, 34387, 34547, 36349, 36503, 36581, 38383, 38503, 38989, 50161, 50903, 50927, 52109, 52303, 52907, 52909, 52961, 54127, 54149, 54389, 54569, 54707, 56323, 56341, 56363, 56387, 56549, 56561, 56723, 56743, 56789, 58301, 58307, 58529, 58547, 58561, 58969, 70303, 70307, 70349, 70523, 70723, 70727, 70747, 72329, 72361, 72389, 72563, 72581, 72929, 72967, 74141, 74329, 74549, 74563, 74909, 74947, 74983, 76121, 76127, 76309, 76327, 76501, 76529, 76729, 76987, 78343, 78383, 78521, 78563, 78581, 78703, 78769, 78961, 90109, 90143, 90347, 90361, 90521, 90581, 90589, 90721, 90743, 90767, 90941, 90943, 90949, 92129, 92303, 92329, 92341, 92501, 92563, 92747, 92749, 94103, 94189, 94301, 94361, 94363, 94763, 94909, 96307, 96361, 96389, 96521, 96721, 96727, 96923, 96983, 98303, 98381, 98503, 98569, 98587, 98723, 98741, 98767, 98783, 98789, 98941, 210367, 210547, 210589, 212321, 212521, 212741, 212767, 212783, 212983, 214103, 214121, 214127, 214369, 214769, 214901, 214969, 216143, 216389, 216527, 216941, 218129, 218321, 218507, 218587, 218903, 230141, 230183, 230509, 230701, 230903, 232147, 232301, 232327, 232343, 232361, 232387, 232721, 232789, 232909, 232949, 234127, 234901, 236123, 236183, 236581, 236903, 236941, 236989, 238367, 238541, 238981, 250127, 250507, 250567, 250981, 252167, 252347, 252521, 252787, 254321, 254503, 254549, 254563, 254701, 254743, 256583, 256769, 256961, 258121, 258169, 258523, 258529, 258749, 270187, 270349, 270703, 272123, 272303, 272309, 272387, 272501, 272543, 272747, 274129, 274181, 274327, 274501, 274507, 274541, 276121, 276169, 276383, 278189, 290363, 290503, 290729, 292121, 292967, 294109, 294527, 296167, 296383, 296501, 296783, 296789, 296903, 298147.

Some larger examples :