23 × 3 × 112
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 121, 132, 242, 264, 363, 484, 726, 968, 1452 and 2904
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.