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amenable n.  and  Proth n.

First numbers that belong to both sets:

5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1025, 1089, 1153, 1217, 1281, 1345, 1409, 1473, 1537, 1601, 1665, 1729, 1793, 1857, 1921, 1985, 2049, 2113, 2177, 2241, 2305, 2369, 2433, 2497, 2561, 2625, 2689, 2753, 2817, 2881, 2945, 3009, 3073, 3137, 3201, 3265, 3329, 3393, 3457, 3521, 3585, 3649, 3713, 3777, 3841, 3905, 3969, 4033, 4097, 4225, 4353, 4481, 4609, 4737, 4865, 4993, 5121, 5249, 5377, 5505, 5633, 5761, 5889, 6017, 6145, 6273, 6401, 6529, 6657, 6785, 6913, 7041, 7169, 7297, 7425, 7553, 7681, 7809, 7937, 8065, 8193, 8321, 8449, 8577, 8705, 8833, 8961, 9089, 9217, 9345, 9473, 9601, 9729, 9857, 9985, 10113, 10241, 10369, 10497, 10625, 10753, 10881, 11009, 11137, 11265, 11393, 11521, 11649, 11777, 11905, 12033, 12161, 12289, 12417, 12545, 12673, 12801, 12929, 13057, 13185, 13313, 13441, 13569, 13697, 13825, 13953, 14081, 14209, 14337, 14465, 14593, 14721, 14849, 14977, 15105, 15233, 15361, 15489, 15617, 15745, 15873, 16001, 16129, 16257, 16385, 16641, 16897, 17153, 17409, 17665, 17921, 18177, 18433, 18689, 18945, 19201, 19457, 19713, 19969, 20225, 20481, 20737, 20993, 21249, 21505, 21761, 22017, 22273, 22529, 22785, 23041, 23297, 23553, 23809, 24065, 24321, 24577, 24833, 25089, 25345, 25601, 25857, 26113, 26369, 26625, 26881, 27137, 27393, 27649, 27905, 28161, 28417, 28673, 28929, 29185, 29441, 29697, 29953, 30209, 30465, 30721, 30977, 31233, 31489, 31745, 32001, 32257, 32513, 32769, 33025, 33281, 33537, 33793, 34049, 34305, 34561, 34817, 35073, 35329, 35585, 35841, 36097, 36353, 36609, 36865, 37121, 37377, 37633, 37889, 38145, 38401, 38657, 38913, 39169, 39425.

Some larger examples :