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Honaker prime  and  odious n.

First numbers that belong to both sets:

131, 457, 1039, 1301, 1361, 1571, 1933, 2273, 2441, 2591, 2663, 3229, 3433, 3559, 4091, 4153, 4723, 4903, 5801, 6301, 6311, 6343, 6553, 6563, 6971, 7213, 7411, 7741, 8011, 8821, 10247, 10559, 10711, 11353, 11701, 11731, 12277, 12347, 13007, 13037, 13217, 13297, 13327, 13339, 13417, 13933, 14437, 14447, 14843, 15193, 15263, 15803, 16073, 16273, 16661, 17317, 17359, 18307, 21617, 22189, 22277, 22613, 23059, 23531, 24091, 24733, 24841, 24971, 25229, 26119, 26209, 26339, 27059, 27091, 29101, 29131, 29243, 29423, 30071, 30091, 30253, 30293, 31177, 31391, 31567, 32059, 32191, 33493, 33533, 34171, 34703, 35027, 35129, 35149, 35327, 35537, 36217, 36307, 36433, 36523, 37019, 37049, 37117, 37783, 38011, 40361, 40427, 40637, 40763, 41131, 41141, 41801, 41941, 42373, 42509, 42737, 43781, 44417, 45119, 45181, 45191, 45821, 45833, 46147, 46237, 48119, 48247, 48463, 49031, 49411, 49531, 50047, 50119, 51131, 51203, 51263, 51421, 52051, 52543, 53407, 53437, 53591, 53881, 54013, 54217, 54617, 55207, 55823, 57059, 57139, 57271, 57943, 58073, 58321, 59183, 60251, 62017, 62057, 62323, 62617, 62627, 63031, 63607, 64151, 64513, 64621, 65371, 65713, 66089, 66301, 67801, 68059, 68147, 69127, 69247, 69257, 69911, 70379, 70459, 71261, 71353, 72337, 74713, 75503, 75941, 76129, 76159, 76403, 77023, 77291, 77339, 77711, 78007, 78283, 78427, 79133, 79273, 79609, 81199, 81239, 82051, 83231, 84067, 87071, 87121, 88007, 88661, 89833, 90163, 91009, 91019, 92251, 92461, 92791, 92861, 94063, 94219, 94229, 96043, 96053, 96443, 96553, 97231, 97711, 98911, 99041, 100279, 100549, 100559, 100957, 101869, 101939, 102397, 102829, 103969, 103979, 105031, 105331, 106031, 106621, 106903, 108037, 109133, 109331, 110129, 110273, 110923, 111229, 111347, 111491, 112153, 112163, 112927, 113027, 113357, 113417, 113591, 113891, 114451, 115561, 115631, 116189, 116257, 117503, 120181, 120511, 120943, 122503, 122533, 123091, 123821, 124153, 124363, 124429, 125029, 125117, 125383, 125423, 125453, 126013.

Some larger examples :