33 × 31 × 37 × 271
1, 3, 9, 27, 31, 37, 93, 111, 271, 279, 333, 813, 837, 999, 1147, 2439, 3441, 7317, 8401, 10027, 10323, 25203, 30081, 30969, 75609, 90243, 226827, 270729, 310837, 932511, 2797533 and 8392599
No.
Its nearest Fibonacci number neighbors are 5702887 and 9227465.