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amenable n.  and  strong prime

First numbers that belong to both sets:

17, 29, 37, 41, 97, 101, 137, 149, 197, 269, 277, 281, 397, 457, 461, 521, 541, 557, 569, 613, 617, 641, 673, 701, 757, 769, 809, 821, 853, 857, 877, 881, 929, 937, 1009, 1049, 1061, 1117, 1181, 1213, 1229, 1249, 1277, 1289, 1297, 1301, 1361, 1481, 1549, 1597, 1657, 1693, 1697, 1721, 1733, 1741, 1777, 1801, 1861, 1877, 1901, 1949, 1973, 1993, 1997, 2053, 2081, 2129, 2137, 2141, 2153, 2237, 2281, 2293, 2309, 2333, 2377, 2381, 2389, 2437, 2473, 2521, 2549, 2609, 2617, 2657, 2729, 2741, 2749, 2789, 2797, 2801, 2833, 2857, 2897, 2953, 2969, 3037, 3061, 3109, 3181, 3217, 3257, 3329, 3389, 3433, 3449, 3457, 3461, 3557, 3581, 3613, 3697, 3761, 3793, 3821, 3877, 3917, 3929, 3989, 4001, 4049, 4073, 4153, 4157, 4201, 4217, 4229, 4241, 4253, 4337, 4349, 4357, 4421, 4441, 4481, 4513, 4517, 4561, 4621, 4637, 4649, 4673, 4721, 4729, 4813, 4861, 5009, 5021, 5077, 5189, 5261, 5273, 5297, 5381, 5413, 5417, 5437, 5441, 5477, 5501, 5557, 5569, 5657, 5689, 5737, 5741, 5801, 5821, 5849, 5857, 5897, 5981, 6029, 6037, 6089, 6113, 6197, 6217, 6257, 6269, 6337, 6353, 6389, 6421, 6449, 6469, 6521, 6569, 6577, 6637, 6653, 6673, 6689, 6701, 6733, 6761, 6857, 6869, 6997, 7013, 7057, 7069, 7121, 7177, 7229, 7237, 7297, 7321, 7349, 7393, 7457, 7477, 7517, 7537, 7573, 7589, 7669, 7681, 7717, 7741, 7753, 7757, 7789, 7817, 7873, 7877, 7901, 7933, 7949, 7993, 8009, 8053, 8081, 8161, 8209, 8269, 8353, 8429, 8461, 8501, 8513, 8521, 8537, 8573, 8597, 8641, 8677, 8689, 8737, 8837, 8861, 8929, 8969, 9029, 9041, 9133, 9157, 9173, 9181, 9221, 9277, 9281, 9337, 9341, 9413, 9437, 9461, 9533, 9601, 9613, 9629, 9677, 9689, 9733, 9781, 9829, 9857, 9901, 9929.

Some larger examples :