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a-pointer prime  and  odious n.

First numbers that belong to both sets:

11, 13, 103, 181, 631, 701, 1153, 1171, 1801, 1933, 2017, 2053, 2143, 2213, 2521, 2633, 3041, 3373, 3391, 3469, 4057, 4231, 5281, 5333, 5717, 6121, 6301, 7043, 7333, 8101, 9241, 10151, 10313, 10463, 11321, 11657, 12241, 12553, 12601, 13729, 15107, 15121, 17011, 17123, 18061, 18313, 18919, 19141, 20129, 20431, 21713, 22921, 23173, 23311, 23719, 25423, 29311, 29641, 31019, 31547, 32203, 32401, 33013, 33091, 33301, 33413, 33811, 35291, 36319, 36353, 37123, 37321, 39521, 39581, 40543, 41117, 41131, 41243, 42307, 43223, 44101, 44389, 44657, 45061, 45139, 46703, 47221, 47317, 48541, 49957, 50023, 50111, 50311, 50513, 50599, 52223, 54001, 54331, 55127, 55291, 56999, 58337, 60413, 60703, 63113, 66271, 66763, 68611, 70207, 70249, 71039, 72139, 72229, 72623, 73651, 74027, 74531, 75583, 75941, 76261, 77291, 79907, 81049, 82051, 82507, 82729, 83357, 84143, 85061, 91309, 92269, 99053, 100333, 100403, 100649, 100801, 100913, 101183, 101363, 101383, 101411, 101503, 102023, 102241, 102913, 103291, 106993, 107123, 109721, 109961, 110051, 110237, 110251, 110543, 111467, 111751, 112459, 112543, 112741, 113041, 114031, 114451, 114691, 115201, 117223, 117731, 118471, 120209, 121453, 122041, 122117, 123017, 123127, 123169, 123457, 123503, 123527, 123833, 124067, 124513, 126001, 126241, 127219, 127507, 130099, 130183, 131221, 131591, 133403, 135241, 136277, 137089, 139313, 140533, 140689, 141079, 141107, 141121, 146449, 147031, 149033, 150413, 150503, 151357, 151609, 151939, 153379, 154213, 154459, 154523, 155047, 155171, 155627, 156019, 157081, 157841, 160603, 161017, 161071, 161611, 162229, 162391, 163367, 164209, 164627, 165181, 165479, 166571, 169501, 170101, 170213, 172127, 173573, 174121, 175081, 175573, 175601, 177511, 177601, 178039, 181141, 181639, 185491, 187141, 188801, 190613, 192347, 194543, 196051, 196927, 198901, 199049, 199153, 200257, 200341, 201557, 202639, 204301, 204679, 204947, 205081, 205171, 205201, 205223, 207199, 208963, 210263, 210283, 210643, 210739, 211231, 211543, 212353, 213097, 214243, 215329, 216289, 218047, 220411, 221401.

Some larger examples :