52 × 11 × 101 × 3001
1, 5, 11, 25, 55, 101, 275, 505, 1111, 2525, 3001, 5555, 15005, 27775, 33011, 75025, 165055, 303101, 825275, 1515505, 3334111, 7577525, 16670555 and 83352775
No.
Its nearest Fibonacci number neighbors are 63245986 and 102334155.