33 × 37 × 41 × 271
1, 3, 9, 27, 37, 41, 111, 123, 271, 333, 369, 813, 999, 1107, 1517, 2439, 4551, 7317, 10027, 11111, 13653, 30081, 33333, 40959, 90243, 99999, 270729, 299997, 411107, 1233321, 3699963 and 11099889
No.
Its nearest Fibonacci number neighbors are 9227465 and 14930352.