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Lehmer n.  and  odious n.

First numbers that belong to both sets:

91, 133, 247, 259, 451, 481, 511, 595, 949, 1261, 1387, 1417, 1615, 1729, 1843, 1891, 2047, 2071, 2091, 2119, 2431, 2465, 2509, 2821, 2955, 3031, 3097, 3145, 3277, 3367, 3589, 3655, 3667, 4033, 4039, 4141, 4411, 4681, 4921, 5083, 5151, 5461, 5551, 5611, 6031, 6205, 6601, 6643, 7141, 7471, 7735, 8071, 8119, 8245, 8401, 8695, 9061, 9079, 9253, 9265, 9367, 9709, 9997, 10213, 10573, 10585, 10795, 12403, 12901, 13021, 13741, 13747, 13855, 13981, 14089, 14611, 14701, 14833, 15051, 15181, 15811, 15841, 16021, 16441, 16531, 16771, 17563, 17611, 18019, 18031, 18151, 18631, 18721, 18745, 18907, 18967, 19345, 19951, 20419, 20595, 20995, 21037, 21679, 21931, 23001, 23281, 24199, 24643, 24727, 24871, 25141, 25351, 26335, 26467, 26599, 27223, 27511, 27721, 28231, 28453, 28645, 28939, 29341, 31171, 31609, 31621, 32407, 32551, 35371, 36661, 36805, 37231, 37921, 38165, 38503, 39491, 40501, 40885, 40921, 41041, 41245, 42001, 43435, 44011, 44317, 45551, 46657, 47197, 47989, 48133, 48709, 49045, 49141, 49231, 49267, 49471, 49567, 49987, 50251, 50737, 50881, 51319, 52429, 52507, 52633, 52801, 53083, 53983, 54223, 54691, 54811, 55423, 55537, 55651, 55699, 55831, 56137, 56551, 57589, 57715, 61249, 62745, 62893, 63973, 64345, 64741, 64771, 65311, 65641, 65683, 66991, 68101, 68191, 68341, 69601, 70579, 71905, 72583, 72631, 73261, 73801, 74011, 74023, 74593, 75055, 75361, 76627, 76741, 76921, 77161, 78013, 78403, 79003, 80665, 80971, 81631, 81691, 82411, 83293, 84169, 86731, 87061, 88621, 88831, 90751, 92491, 92701, 92929, 93031, 93805, 93961, 93991, 94051, 94831, 96139, 96691, 96985, 97921, 98623, 98671, 98881, 102277, 104653, 104923, 106141, 106951, 107929, 109291, 109861, 111055, 111361, 111841, 112141, 112147, 113201, 113821, 114589, 114835, 115231, 116935, 117181, 117895, 118027, 118405, 119461, 120171, 121435, 122479, 123151, 124015, 124645, 125341, 125401, 125809, 126133, 126217, 126331, 126673, 126701, 127909.

Some larger examples :