32 × 37 × 41 × 271
1, 3, 9, 37, 41, 111, 123, 271, 333, 369, 813, 1517, 2439, 4551, 10027, 11111, 13653, 30081, 33333, 90243, 99999, 411107, 1233321 and 3699963
No.
Its nearest Fibonacci number neighbors are 3524578 and 5702887.