32 × 13 × 37 × 101
1, 3, 9, 13, 37, 39, 101, 111, 117, 303, 333, 481, 909, 1313, 1443, 3737, 3939, 4329, 11211, 11817, 33633, 48581, 145743 and 437229
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.