3 × 7 × 43 × 127 × 337
1, 3, 7, 21, 43, 127, 129, 301, 337, 381, 889, 903, 1011, 2359, 2667, 5461, 7077, 14491, 16383, 38227, 42799, 43473, 101437, 114681, 128397, 299593, 304311, 898779, 1840357, 5521071, 12882499 and 38647497
No.
Its nearest Fibonacci number neighbors are 24157817 and 39088169.