22 × 3 × 7 × 37
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 37, 42, 74, 84, 111, 148, 222, 259, 444, 518, 777, 1036, 1554 and 3108
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.