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Chen prime  and  balanced n.

First numbers that belong to both sets:

2, 11, 19, 37, 41, 139, 149, 197, 541, 557, 563, 569, 587, 617, 647, 653, 659, 677, 787, 809, 2141, 2251, 2281, 2333, 2357, 2381, 2389, 2393, 2417, 2467, 2659, 2699, 2729, 2837, 2857, 2897, 3221, 3347, 3461, 6791, 6911, 6947, 6959, 7001, 7039, 7151, 7193, 7247, 7433, 7487, 7499, 7517, 7559, 7607, 7793, 7877, 7949, 8069, 8087, 8117, 8147, 8219, 8297, 8429, 8527, 8537, 8543, 8597, 8627, 8681, 8689, 8807, 8819, 8861, 8933, 8969, 8999, 9011, 9109, 9209, 9257, 9281, 9419, 9551, 9649, 9743, 9767, 9811, 9929, 10271, 10301, 10331, 10343, 10391, 10457, 10597, 10601, 10711, 10781, 10837, 10891, 10949, 10979, 11027, 11057, 11213, 11279, 11351, 11369, 11399, 11411, 11467, 11489, 11587, 11657, 11681, 11699, 11783, 11789, 11831, 11909, 11927, 11969, 12037, 12041, 12071, 12161, 12347, 12379, 12457, 12479, 12601, 12641, 12713, 12721, 12889, 12953, 13001, 13009, 13217, 13339, 13397, 13441, 13451, 13463, 13469, 13477, 13537, 13721, 13807, 13859, 13901, 13967, 13997, 14071, 14369, 14387, 14401, 14437, 14447, 14449, 14489, 14561, 14621, 14627, 14629, 14633, 14699, 14867, 14869, 14897, 15107, 15137, 15359, 15401, 15413, 15497, 15569, 15641, 15809, 15817, 15881, 15887, 15889, 16001, 16061, 16097, 16103, 16127, 16139, 16229, 16529, 16607, 17021, 17599, 17609, 18311, 18397, 33119, 33149, 33211, 33391, 33529, 33749, 33769, 33911, 34127, 34157, 34259, 34421, 34471, 34583, 34589, 34631, 34649, 34757, 35051, 35159, 35227, 35419, 35437, 35507, 35531, 35747, 35753, 35933, 36011, 36629, 36677, 37039, 37199, 37277, 37337, 37361, 37493, 37547, 37549, 37579, 37589, 37781, 37967, 37991, 38039, 38069, 38189, 38219, 38321, 38453, 38501, 38609, 38669, 38677, 39019, 39097, 39239, 39251, 39439, 39451, 39509, 39749, 39761, 39979, 40037, 40099, 40241, 40289, 40459, 40529, 40609, 40709, 41387, 41519, 41579, 41651, 41771, 41813, 42071, 42101, 42169, 42197.

Some larger examples :