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Honaker prime  and  pernicious n.

First numbers that belong to both sets:

131, 457, 1039, 1301, 1361, 1571, 1933, 2273, 2441, 2591, 2663, 3229, 3433, 4091, 4153, 4723, 4903, 5801, 6301, 6311, 6343, 6553, 6563, 7213, 8821, 10247, 11353, 12277, 12347, 13217, 13327, 13339, 13417, 14437, 14843, 15263, 15803, 16661, 17317, 18307, 21617, 22277, 22613, 23059, 23531, 24733, 24841, 24971, 25229, 26119, 26209, 29423, 30071, 31391, 31567, 32059, 32191, 33493, 35027, 35129, 35149, 35327, 35537, 36433, 37019, 37049, 40427, 40637, 40763, 41131, 41141, 41801, 42373, 42509, 43781, 44417, 45191, 45821, 45833, 46147, 48119, 48247, 48463, 49031, 49411, 50047, 51131, 51203, 52543, 54013, 55207, 57059, 57139, 57271, 59183, 60251, 62017, 62323, 63031, 63607, 64151, 64513, 64621, 65371, 65713, 66089, 67801, 68147, 69127, 69247, 69257, 69911, 72337, 75503, 75941, 76129, 76159, 77023, 77291, 77711, 79609, 81199, 81239, 82051, 84067, 87121, 88007, 89833, 90163, 91009, 92791, 92861, 94063, 94219, 94229, 96043, 96053, 96443, 97231, 97711, 99041, 100279, 100549, 101869, 102397, 103969, 105331, 106031, 108037, 111229, 111347, 112927, 113357, 113591, 113891, 114451, 115631, 116189, 116257, 117503, 120181, 120511, 120943, 122503, 122533, 123821, 124153, 124363, 125117, 125383, 125423, 126013, 126143, 126271, 126517, 126653, 127423, 130087, 130183, 131213, 132233, 132313, 132607, 132721, 133213, 133241, 133271, 133451, 133801, 135731, 136207, 136237, 136277, 138113, 138241, 139123, 139409, 140423, 140453, 141301, 142403, 143357, 143443, 145207, 145661, 147047, 149183, 149251, 151537, 151597, 151609, 156127, 157307, 157561, 159403, 160603, 162109, 163117, 163147, 163481, 164621, 170447, 170711, 171641, 171671, 171761, 171881, 173137, 174091, 174767, 175039, 175229, 175453, 175463, 175843, 178301, 178351, 180241, 180281, 181211, 182233, 182341, 182417, 183119, 183301, 183503, 184187, 185149, 185267, 185327, 185519, 186727, 187127, 187711, 192461, 194413, 196081, 196247, 196307, 196429, 197273, 201709, 201809, 202049, 203227, 204461, 204733, 204781, 205783, 212627, 213751, 214507, 214517, 215981, 216523, 216917, 217169, 218461, 218549, 218923.

Some larger examples :