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a-pointer prime  and  evil n.

First numbers that belong to both sets:

101, 293, 811, 1409, 2039, 3089, 3221, 3643, 3739, 5153, 5449, 5623, 6053, 8543, 10667, 11161, 12203, 12401, 13381, 13523, 13633, 14087, 14177, 14207, 15017, 15413, 15473, 17761, 18461, 20369, 21023, 21601, 21803, 22093, 22453, 22501, 23003, 23117, 24181, 24923, 25771, 27043, 30119, 30203, 30469, 30713, 33941, 36607, 37253, 38351, 41203, 41737, 41911, 43003, 43117, 43207, 43913, 44071, 46831, 49081, 50207, 50627, 51691, 51871, 52267, 53381, 53507, 53527, 54421, 54601, 54881, 56401, 57529, 61153, 62327, 63443, 64189, 64303, 71671, 71741, 73433, 76441, 77813, 80491, 80963, 81773, 83117, 83177, 83663, 84349, 84761, 88301, 89021, 89533, 90203, 91163, 91433, 92153, 92203, 93503, 100193, 101141, 101323, 101723, 101749, 102061, 102481, 103217, 103529, 104513, 104597, 104623, 105541, 107323, 107903, 108023, 108139, 108649, 111623, 112103, 112121, 112213, 113467, 114143, 115223, 117023, 118127, 119513, 120223, 121507, 121967, 122719, 123239, 126047, 127343, 127781, 128221, 128629, 131203, 132383, 133283, 133519, 133999, 134417, 135979, 136013, 140207, 140281, 144139, 144791, 145361, 145549, 148171, 148207, 151397, 153287, 155027, 155423, 156749, 157061, 160001, 160841, 161123, 163697, 164023, 165673, 166043, 166429, 167051, 170299, 170927, 171007, 172721, 173023, 174169, 176651, 180007, 180391, 180751, 181039, 181253, 184133, 185189, 185651, 186317, 192013, 193261, 197713, 198503, 198859, 200033, 201287, 201403, 202343, 202529, 204563, 207241, 207593, 209861, 210131, 210173, 210193, 210407, 211051, 211349, 211619, 212131, 212423, 214021, 216023, 216133, 216919, 218171, 218191, 218401, 219103, 222679, 223339, 226013, 228383, 230063, 230203, 230663, 233143, 233251, 233297, 237707, 240073, 240769, 241711, 242419, 243931, 244507, 244639, 245683, 247553, 248141, 251297, 254119, 256771, 257141, 259277, 260651, 261043, 261407, 262981, 264013, 265313, 269351, 270379, 270421, 271367, 273233, 274751, 277961, 280561, 281207, 281807, 285317, 287191, 287821, 287939, 288109, 291299, 291901, 296519, 299213, 300089, 300221, 301127, 302173, 302609, 303781, 306331, 313133, 315421, 316271, 316343, 316471, 316819.

Some larger examples :