22 × 3 × 7 × 11
1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462 and 924
No.
Its nearest Fibonacci number neighbors are 610 and 987.