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a-pointer prime  and  amenable n.

First numbers that belong to both sets:

13, 101, 181, 293, 701, 1153, 1409, 1801, 1933, 2017, 2053, 2213, 2521, 2633, 3041, 3089, 3221, 3373, 3469, 4057, 5153, 5281, 5333, 5449, 5717, 6053, 6121, 6301, 7333, 8101, 9241, 10313, 11161, 11321, 11657, 12241, 12401, 12553, 12601, 13381, 13633, 13729, 14177, 15017, 15121, 15413, 15473, 17761, 18061, 18313, 18461, 19141, 20129, 20369, 21601, 21713, 22093, 22453, 22501, 22921, 23117, 23173, 24181, 29641, 30469, 30713, 32401, 33013, 33301, 33413, 33941, 36353, 37253, 37321, 39521, 39581, 41117, 41737, 43117, 43913, 44101, 44389, 44657, 45061, 47221, 47317, 48541, 49081, 49957, 50513, 53381, 54001, 54421, 54601, 54881, 56401, 57529, 58337, 60413, 61153, 63113, 64189, 70249, 71741, 72229, 73433, 75941, 76261, 76441, 77813, 81049, 81773, 82729, 83117, 83177, 83357, 84349, 84761, 85061, 88301, 89021, 89533, 91309, 91433, 92153, 92269, 99053, 100193, 100333, 100649, 100801, 100913, 101141, 101749, 102061, 102241, 102481, 102913, 103217, 103529, 104513, 104597, 105541, 106993, 108649, 109721, 109961, 110237, 112121, 112213, 112741, 113041, 115201, 119513, 120209, 121453, 122041, 122117, 123017, 123169, 123457, 123833, 124513, 126001, 126241, 127781, 128221, 128629, 131221, 134417, 135241, 136013, 136277, 137089, 139313, 140281, 140533, 140689, 141121, 145361, 145549, 146449, 149033, 150413, 151357, 151397, 151609, 154213, 156749, 157061, 157081, 157841, 160001, 160841, 161017, 162229, 163697, 164209, 165181, 165673, 166429, 169501, 170101, 170213, 172721, 173573, 174121, 174169, 175081, 175573, 175601, 177601, 181141, 181253, 184133, 185189, 186317, 187141, 188801, 190613, 192013, 193261, 197713, 198901, 199049, 199153, 200033, 200257, 200341, 201557, 202529, 204301, 205081, 205201, 207241, 207593, 209861, 210173, 210193, 211349, 212353, 213097, 214021, 215329, 216133, 216289, 218401, 221401, 225241, 226013, 231053, 233297, 235369, 237581, 239297, 240073, 240101, 240769, 241229, 241517, 242309, 245593, 247553, 247913, 247957, 248141, 250153, 251297, 253613, 255217, 256661, 257141, 257921, 259277, 260893, 260921, 261281, 262909, 262981, 264013.

Some larger examples :