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evil n.  and  Lehmer n.

First numbers that belong to both sets:

15, 51, 85, 255, 435, 561, 679, 703, 763, 771, 1105, 1111, 1141, 1285, 1351, 1695, 2701, 2761, 3409, 3855, 4369, 4795, 5383, 5629, 5713, 6331, 6735, 7051, 7081, 7501, 7957, 8227, 8481, 8827, 8911, 8995, 9139, 9211, 9605, 9919, 10291, 10963, 11041, 11155, 11305, 11899, 12801, 13107, 13333, 13651, 14491, 14497, 14911, 14989, 15211, 16297, 16405, 16471, 16705, 16745, 16861, 17733, 17767, 19669, 20451, 21349, 21845, 21907, 22015, 22261, 22321, 22359, 23959, 24415, 24661, 25123, 25669, 26281, 26923, 27331, 30481, 30583, 30889, 31417, 31459, 31611, 32215, 32691, 33001, 33709, 34441, 34861, 35113, 35551, 35881, 36091, 36391, 36499, 36751, 37969, 39091, 39403, 39817, 39831, 39865, 40261, 41395, 41881, 42121, 42127, 42217, 42661, 42799, 43165, 43387, 43621, 44941, 45811, 45991, 47055, 47239, 47545, 47671, 49051, 49155, 49771, 50557, 53131, 54741, 55471, 55969, 56661, 56797, 57205, 59641, 59755, 63139, 63631, 64201, 64855, 65365, 65535, 67771, 68251, 68619, 69231, 69751, 69781, 69979, 72535, 73555, 73891, 74665, 77871, 79381, 81651, 83011, 83569, 83665, 83731, 83821, 85471, 85591, 85695, 85765, 86023, 87123, 88357, 88453, 88561, 90973, 91001, 92053, 92833, 94657, 94681, 95941, 97351, 97567, 98005, 99499, 100651, 101101, 101311, 101935, 103441, 105001, 106507, 107185, 108691, 108781, 110245, 110371, 110677, 113401, 113611, 115627, 115921, 116705, 120289, 120445, 122221, 122461, 124369, 125347, 125563, 125581, 125677, 127723, 128371, 129795, 130381, 131821, 132769, 134539, 134797, 135931, 136981, 137449, 137971, 140065, 140911, 141373, 141523, 141571, 142519, 145027, 145993, 146611, 147109, 147259, 148831, 150691, 151183, 153349, 156655, 157641, 159259, 160291, 161653, 162955, 163885, 163891, 164041, 164761, 167713, 168103, 170431, 170905, 172081, 172291, 173419, 180115, 180991, 182527, 184255, 184891, 187939, 188461, 189289, 190411, 193249, 193521, 194701, 195451, 196261, 196611, 196651, 196981, 199171, 200431, 204841, 205465, 205543, 206371, 206521, 209455, 211191, 211531, 211555.

Some larger examples :