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a-pointer prime  and  cyclic n.

First numbers that belong to both sets:

11, 13, 101, 103, 181, 293, 631, 701, 811, 1153, 1171, 1409, 1801, 1933, 2017, 2039, 2053, 2143, 2213, 2521, 2633, 3041, 3089, 3221, 3373, 3391, 3469, 3643, 3739, 4057, 4231, 5153, 5281, 5333, 5449, 5623, 5717, 6053, 6121, 6301, 7043, 7333, 8101, 8543, 9241, 10151, 10313, 10463, 10667, 11161, 11321, 11657, 12203, 12241, 12401, 12553, 12601, 13381, 13523, 13633, 13729, 14087, 14177, 14207, 15017, 15107, 15121, 15413, 15473, 17011, 17123, 17761, 18061, 18313, 18461, 18919, 19141, 20129, 20369, 20431, 21023, 21601, 21713, 21803, 22093, 22453, 22501, 22921, 23003, 23117, 23173, 23311, 23719, 24181, 24923, 25423, 25771, 27043, 29311, 29641, 30119, 30203, 30469, 30713, 31019, 31547, 32203, 32401, 33013, 33091, 33301, 33413, 33811, 33941, 35291, 36319, 36353, 36607, 37123, 37253, 37321, 38351, 39521, 39581, 40543, 41117, 41131, 41203, 41243, 41737, 41911, 42307, 43003, 43117, 43207, 43223, 43913, 44071, 44101, 44389, 44657, 45061, 45139, 46703, 46831, 47221, 47317, 48541, 49081, 49957, 50023, 50111, 50207, 50311, 50513, 50599, 50627, 51691, 51871, 52223, 52267, 53381, 53507, 53527, 54001, 54331, 54421, 54601, 54881, 55127, 55291, 56401, 56999, 57529, 58337, 60413, 60703, 61153, 62327, 63113, 63443, 64189, 64303, 66271, 66763, 68611, 70207, 70249, 71039, 71671, 71741, 72139, 72229, 72623, 73433, 73651, 74027, 74531, 75583, 75941, 76261, 76441, 77291, 77813, 79907, 80491, 80963, 81049, 81773, 82051, 82507, 82729, 83117, 83177, 83357, 83663, 84143, 84349, 84761, 85061, 88301, 89021, 89533, 90203, 91163, 91309, 91433, 92153, 92203, 92269, 93503, 99053, 100193, 100333, 100403, 100649, 100801, 100913, 101141, 101183, 101323, 101363, 101383, 101411, 101503, 101723, 101749, 102023, 102061, 102241, 102481, 102913, 103217, 103291, 103529, 104513, 104597, 104623, 105541, 106993, 107123, 107323, 107903, 108023, 108139, 108649, 109721, 109961, 110051, 110237, 110251, 110543, 111467, 111623, 111751, 112103, 112121, 112213, 112459, 112543.

Some larger examples :