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congruent n.  and  Honaker prime

First numbers that belong to both sets:

263, 457, 1039, 1301, 1933, 2141, 2221, 2273, 2591, 2663, 2719, 3229, 3433, 3559, 3631, 4357, 4397, 4703, 4903, 5701, 5711, 5741, 5927, 6301, 6311, 6343, 6653, 7013, 7213, 7741, 8821, 9103, 10247, 10429, 10559, 10711, 11071, 11173, 11701, 11821, 12277, 12613, 13007, 13037, 13127, 13327, 13367, 13933, 14159, 14437, 14447, 15173, 15263, 15671, 15761, 16661, 17159, 17189, 17317, 17359, 18013, 20533, 20543, 22189, 22277, 22613, 22807, 24733, 25229, 26119, 26189, 26209, 26309, 27277, 29023, 29101, 29423, 30071, 30253, 30293, 31391, 31517, 31567, 32029, 32191, 32261, 33493, 33533, 34471, 34543, 34703, 35129, 35149, 35327, 35537, 37039, 37117, 37463, 37493, 37717, 37783, 38711, 40637, 40823, 41141, 41333, 41801, 41941, 42373, 42509, 42727, 42737, 43543, 43781, 44221, 45119, 45181, 45191, 45821, 46237, 47293, 47623, 48109, 48119, 48247, 48463, 49031, 50047, 50119, 51263, 51421, 52543, 52733, 53309, 53407, 53437, 53591, 54013, 54727, 54941, 55207, 55541, 55733, 55823, 56807, 57119, 57271, 57301, 57943, 59093, 59183, 61253, 61703, 62303, 63031, 63607, 64151, 64231, 64621, 65831, 66089, 66301, 67073, 68813, 68903, 69127, 69247, 69383, 69463, 69911, 70039, 70079, 71261, 72701, 73607, 74231, 75503, 75941, 76159, 76423, 77023, 77237, 77711, 77813, 78007, 78437, 79133, 79333, 81199, 81239, 82207, 82813, 83231, 83311, 85093, 85133, 87013, 87071, 87151, 88007, 88661, 90173, 90469, 90647, 91583, 92461, 92791, 92861, 94063, 94151, 94229, 94327, 95111, 96053, 97103, 97151, 97231, 97241, 97711, 98911, 100279, 100549, 100559, 100957, 101869, 102359, 102397, 102829, 103969, 105031, 106031, 106621, 106903, 108037, 109103, 109133, 110119, 110129, 110813, 111053, 111229, 112927, 113327, 113357, 113417, 113591, 115631, 115853, 116159, 116189, 117503, 120181, 120511, 120709, 120943, 122471, 122503, 122533, 123701, 123733, 123821, 124183, 124429, 125029, 125117, 125383, 125423, 125453, 126013, 126143, 126271, 126517, 126653, 127423, 127681, 127733, 129221, 130087, 130183, 131213.

Some larger examples :