22 × 3 × 11 × 19
1, 2, 3, 4, 6, 11, 12, 19, 22, 33, 38, 44, 57, 66, 76, 114, 132, 209, 228, 418, 627, 836, 1254 and 2508
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.