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alternating n.  and  Chen prime

First numbers that belong to both sets:

2, 3, 5, 7, 23, 29, 41, 47, 67, 83, 89, 101, 107, 109, 127, 149, 167, 181, 307, 347, 389, 503, 509, 521, 541, 563, 569, 587, 701, 743, 761, 769, 787, 941, 947, 983, 2129, 2141, 2309, 2381, 2389, 2543, 2549, 2729, 2741, 2789, 2909, 2927, 2963, 2969, 4127, 4349, 4547, 4567, 4703, 4721, 4787, 4789, 4909, 4967, 4969, 4987, 6101, 6143, 6329, 6521, 6569, 6581, 6701, 6709, 6761, 6947, 8147, 8329, 8369, 8387, 8389, 8501, 8527, 8543, 8581, 8707, 8741, 8747, 8969, 10169, 10181, 10301, 10343, 10369, 10529, 10709, 10781, 10909, 10949, 12107, 12149, 12161, 12347, 12569, 12721, 12743, 12781, 14107, 14303, 14321, 14347, 14369, 14387, 14543, 14549, 14561, 14741, 14783, 14969, 16103, 16127, 16141, 16187, 16349, 16361, 16529, 16561, 16741, 16787, 16901, 16921, 16943, 18127, 18149, 18301, 18329, 18503, 18521, 18587, 18701, 18749, 18787, 18947, 30109, 30181, 30307, 30341, 30389, 30509, 30529, 30727, 30983, 32141, 32189, 32309, 32321, 32327, 32341, 32363, 32369, 32561, 32707, 32909, 32969, 32987, 34127, 34147, 34301, 34327, 34361, 34367, 34583, 34589, 34721, 34781, 34949, 34961, 36107, 36109, 36341, 36389, 36527, 36587, 36721, 36761, 36767, 36787, 36901, 36929, 36947, 38189, 38321, 38327, 38501, 38567, 38747, 38749, 38767, 38783, 38921, 50129, 50387, 50527, 50549, 50707, 50789, 50969, 52121, 52147, 52163, 52181, 52301, 52361, 52529, 52541, 52709, 52721, 52727, 52769, 52901, 54121, 54167, 54181, 54361, 54521, 54541, 54581, 56101, 56369, 56501, 56909, 56921, 56963, 58109, 58169, 58321, 58367, 58369, 58787, 58789, 58907, 58943, 58967, 70121, 70163, 70181, 70529, 70589, 70709, 70949, 72101, 72167, 72307, 72341, 72767, 72949, 74381, 74507, 74521, 74561, 74567, 74729, 74747, 74929, 76163, 76343, 76367, 76369, 76387, 76541, 76907, 76949, 76961, 78101, 78121, 78341, 78347, 78509, 78569, 78707, 78781, 78787, 78929, 78941.

Some larger examples :