33 × 31 × 37 × 41
1, 3, 9, 27, 31, 37, 41, 93, 111, 123, 279, 333, 369, 837, 999, 1107, 1147, 1271, 1517, 3441, 3813, 4551, 10323, 11439, 13653, 30969, 34317, 40959, 47027, 141081, 423243 and 1269729
No.
Its nearest Fibonacci number neighbors are 832040 and 1346269.