2 × 52 × 7 × 11
1, 2, 5, 7, 10, 11, 14, 22, 25, 35, 50, 55, 70, 77, 110, 154, 175, 275, 350, 385, 550, 770, 1925 and 3850
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.