3 × 29 × 43 × 113 × 127
1, 3, 29, 43, 87, 113, 127, 129, 339, 381, 1247, 3277, 3683, 3741, 4859, 5461, 9831, 11049, 14351, 14577, 16383, 43053, 140911, 158369, 416179, 422733, 475107, 617093, 1248537, 1851279, 17895697 and 53687091
No.
Its nearest Fibonacci number neighbors are 39088169 and 63245986.