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amenable n.  and  good prime

First numbers that belong to both sets:

5, 17, 29, 37, 41, 53, 97, 101, 149, 257, 269, 541, 557, 569, 593, 641, 733, 809, 821, 853, 929, 937, 1009, 1213, 1277, 1597, 1861, 1973, 1993, 1997, 2237, 2333, 2521, 2609, 2657, 2677, 3433, 3449, 3457, 3461, 3821, 3989, 4001, 4201, 4217, 4229, 4441, 4481, 4621, 4637, 4861, 5381, 5413, 6029, 6037, 6197, 6257, 6521, 6637, 6653, 6689, 6761, 7457, 7477, 7517, 7537, 8053, 8081, 8161, 8209, 8501, 8513, 8521, 8597, 8677, 8689, 9133, 9277, 9337, 9397, 9413, 9613, 10037, 10061, 10133, 10589, 10597, 10853, 11057, 11657, 11677, 11777, 11897, 12197, 12373, 12377, 12473, 12889, 13669, 14293, 14321, 14369, 14401, 14533, 14713, 15013, 15053, 15073, 15217, 15269, 16417, 16829, 17317, 17377, 17837, 17881, 17909, 19001, 19373, 19417, 19421, 19889, 19913, 19961, 20681, 20717, 20849, 20873, 20897, 20981, 21313, 21377, 21481, 21557, 22541, 22613, 22637, 22697, 22961, 23497, 23537, 23549, 23557, 23741, 24841, 24917, 25117, 25301, 25537, 25561, 25577, 25913, 26669, 26681, 27397, 27673, 27689, 27733, 27737, 28277, 28493, 28537, 28597, 29833, 30089, 30637, 30757, 31121, 31957, 32057, 32297, 32969, 33329, 35729, 35797, 35801, 36433, 38113, 38149, 38177, 38557, 38593, 38669, 39089, 40693, 40697, 40801, 40813, 41113, 41141, 41177, 41513, 41593, 41849, 41941, 43573, 43577, 43889, 43933, 43961, 44449, 44497, 45817, 46021, 46049, 46133, 46141, 46993, 47041, 47269, 47293, 47497, 48337, 48397, 48473, 48757, 48973, 48989, 50741, 50821, 50833, 51109, 51193, 51197, 51329, 51341, 51413, 52501, 52529, 52541, 54269, 54361, 54401, 55661, 55793, 56369, 56377, 56437, 56473, 58889, 58897, 60589, 60601, 61253, 61441, 61469, 63241, 63277, 64553, 64577, 64601, 64849, 64877, 64997, 65089, 65353, 65537, 66293, 66337, 66449, 66457, 66697, 66841, 67033, 67121, 69653, 69677, 69737, 69761, 69809, 69821, 69997, 70001, 70117, 70841, 70913, 71233, 73277, 73361, 73517.

Some larger examples :