22 × 3 × 11 × 29
1, 2, 3, 4, 6, 11, 12, 22, 29, 33, 44, 58, 66, 87, 116, 132, 174, 319, 348, 638, 957, 1276, 1914 and 3828
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.