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amenable n.  and  Sophie Germain prime

First numbers that belong to both sets:

5, 29, 41, 53, 89, 113, 173, 233, 281, 293, 509, 593, 641, 653, 761, 809, 953, 1013, 1049, 1229, 1289, 1409, 1481, 1601, 1733, 1889, 1901, 1973, 2069, 2129, 2141, 2273, 2393, 2549, 2693, 2741, 2753, 2969, 3329, 3389, 3413, 3449, 3593, 3761, 3821, 4073, 4349, 4373, 4409, 4481, 4733, 4793, 5081, 5333, 5441, 5501, 5741, 5849, 6053, 6101, 6113, 6173, 6269, 6329, 6449, 6521, 6581, 6761, 7121, 7193, 7349, 7433, 7541, 7649, 7841, 7901, 8069, 8093, 8273, 8513, 8693, 8741, 8969, 9029, 9221, 9293, 9473, 9629, 9689, 10061, 10253, 10313, 10529, 10589, 10613, 10709, 10733, 10781, 11321, 11369, 11393, 11549, 11801, 11813, 11909, 12041, 12101, 12329, 12653, 12821, 13001, 13049, 13229, 13313, 13553, 13649, 13901, 13913, 14009, 14081, 14153, 14249, 14321, 14489, 14561, 14621, 14669, 14741, 15101, 15161, 15173, 15233, 15269, 15401, 15569, 15629, 15773, 16001, 16253, 16301, 16421, 16493, 16553, 16673, 17333, 17669, 17681, 17981, 18041, 18149, 18233, 18341, 18461, 18773, 19301, 19373, 19433, 19553, 19661, 19709, 19889, 19913, 20249, 20369, 20393, 20441, 20693, 20753, 20789, 20921, 21089, 21149, 21221, 21341, 21701, 21713, 21893, 22013, 22133, 22349, 22409, 22433, 22469, 22481, 22541, 22853, 23321, 23561, 23669, 23753, 23909, 23981, 24281, 24473, 24509, 24749, 25073, 25229, 25601, 25673, 25841, 25913, 26189, 26501, 26573, 26633, 26849, 26993, 27281, 27581, 27773, 27809, 27893, 28001, 28793, 28901, 28949, 28961, 29021, 29033, 29201, 29453, 29873, 30269, 30389, 30449, 30689, 30773, 31253, 31469, 31649, 31721, 31793, 32009, 32141, 32381, 32561, 32573, 32633, 32789, 32933, 33053, 33461, 33521, 33569, 33713, 33749, 33773, 33809, 33941, 34253, 34913, 34949, 35069, 35081, 35573, 35933, 35993, 36353, 36629, 36761, 36821, 36929, 37013, 37049, 37181, 37253, 37853, 38189, 38201, 38333, 38453, 38501, 38669, 38861, 38873, 38933, 39089, 39233, 39521.

Some larger examples :