3 × 5 × 29 × 113 × 127
1, 3, 5, 15, 29, 87, 113, 127, 145, 339, 381, 435, 565, 635, 1695, 1905, 3277, 3683, 9831, 11049, 14351, 16385, 18415, 43053, 49155, 55245, 71755, 215265, 416179, 1248537, 2080895 and 6242685
No.
Its nearest Fibonacci number neighbors are 5702887 and 9227465.