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amenable n.  and  twin primes

First numbers that belong to both sets:

5, 13, 17, 29, 41, 61, 73, 101, 109, 137, 149, 181, 193, 197, 229, 241, 269, 281, 313, 349, 421, 433, 461, 521, 569, 601, 617, 641, 661, 809, 821, 829, 857, 881, 1021, 1033, 1049, 1061, 1093, 1153, 1229, 1277, 1289, 1301, 1321, 1429, 1453, 1481, 1489, 1609, 1621, 1669, 1697, 1721, 1789, 1873, 1877, 1933, 1949, 1997, 2029, 2081, 2089, 2113, 2129, 2141, 2237, 2269, 2309, 2341, 2381, 2549, 2593, 2657, 2689, 2713, 2729, 2789, 2801, 2969, 3001, 3121, 3169, 3253, 3257, 3301, 3329, 3361, 3373, 3389, 3461, 3469, 3529, 3541, 3557, 3581, 3673, 3769, 3821, 3853, 3917, 3929, 4001, 4021, 4049, 4093, 4129, 4157, 4217, 4229, 4241, 4261, 4273, 4337, 4421, 4481, 4517, 4549, 4637, 4649, 4721, 4789, 4801, 4933, 4969, 5009, 5021, 5101, 5233, 5281, 5417, 5441, 5477, 5501, 5521, 5641, 5653, 5657, 5741, 5849, 5869, 5881, 6089, 6133, 6197, 6269, 6301, 6361, 6449, 6553, 6569, 6661, 6689, 6701, 6761, 6781, 6793, 6829, 6869, 6949, 6961, 7129, 7213, 7309, 7333, 7349, 7457, 7489, 7549, 7561, 7589, 7757, 7877, 7949, 8009, 8089, 8221, 8233, 8293, 8389, 8429, 8537, 8597, 8629, 8821, 8837, 8861, 8969, 9001, 9013, 9041, 9241, 9281, 9341, 9421, 9433, 9437, 9461, 9629, 9677, 9721, 9769, 9857, 9929, 10009, 10037, 10069, 10093, 10141, 10273, 10301, 10333, 10429, 10457, 10501, 10529, 10709, 10861, 10889, 10937, 11057, 11069, 11117, 11161, 11173, 11353, 11489, 11549, 11701, 11717, 11777, 11833, 11941, 11969, 12041, 12073, 12109, 12161, 12241, 12253, 12377, 12541, 12613, 12821, 12917, 13001, 13009, 13217, 13337, 13397, 13681, 13693, 13709, 13721, 13757, 13829, 13877, 13901, 13933, 13997, 14009, 14081, 14249, 14321, 14389, 14449, 14549, 14561, 14593, 14629, 14869, 15137, 15269, 15289, 15329, 15361, 15581, 15641, 15649, 15733.

Some larger examples :