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amenable n.  and  Honaker prime

First numbers that belong to both sets:

457, 1049, 1301, 1361, 1433, 1913, 1933, 2141, 2221, 2273, 2441, 2729, 3137, 3229, 3433, 4153, 4357, 4397, 5009, 5701, 5741, 5801, 6301, 6353, 6553, 6653, 6737, 7013, 7213, 7481, 7741, 8821, 10429, 11173, 11353, 11701, 11821, 12277, 12613, 13037, 13217, 13297, 13417, 13457, 13933, 14437, 15173, 15193, 15761, 15913, 16073, 16193, 16273, 16661, 17189, 17317, 18013, 18041, 20533, 21617, 22189, 22277, 22613, 24733, 24841, 25229, 26189, 26209, 26309, 27277, 29101, 30253, 30293, 31177, 31517, 32009, 32029, 32261, 33493, 33533, 35129, 35149, 35537, 35617, 36217, 36433, 37049, 37117, 37493, 37717, 40361, 40637, 41141, 41333, 41801, 41941, 42373, 42509, 42737, 43781, 44221, 44417, 45181, 45821, 45833, 46237, 47017, 47293, 48109, 48473, 50417, 51421, 51473, 52553, 52733, 53309, 53437, 53881, 54013, 54217, 54617, 54941, 55049, 55541, 55733, 57089, 57301, 57713, 58073, 58321, 58921, 59093, 60601, 61253, 62017, 62057, 62273, 62617, 63313, 64513, 64621, 64817, 65713, 66089, 66301, 67073, 67801, 68813, 69257, 70489, 71261, 71353, 72337, 72701, 73009, 74713, 75941, 76129, 77237, 77249, 77813, 78017, 78437, 79133, 79273, 79333, 79609, 80657, 82217, 82813, 84017, 84313, 85081, 85093, 85133, 86113, 87013, 87121, 88661, 89833, 90173, 90469, 91009, 92461, 92861, 93097, 94033, 94229, 96053, 96553, 97241, 99041, 100549, 100957, 101869, 101929, 102397, 102829, 103969, 106621, 108037, 109133, 109321, 110129, 110273, 110813, 111053, 111229, 112153, 113357, 113417, 114809, 115561, 115601, 115853, 116089, 116189, 116257, 120181, 120473, 120709, 122533, 123217, 123701, 123733, 123821, 124153, 124193, 124429, 125029, 125117, 125453, 126013, 126517, 126653, 127681, 127733, 129113, 129221, 131009, 131213, 131381, 132233, 132313, 132541, 132721, 133153, 133213, 133241, 133261, 133801, 134741, 136177, 136217, 136237, 136277, 136337, 136621, 137437, 138113, 138241, 139133, 139201, 139409, 140453, 141161, 141241, 141301, 143357, 145121, 145441, 145513, 145661, 145721, 149113, 149173, 150197, 151337, 151537, 151597.

Some larger examples :