22 × 3 × 11 × 23
1, 2, 3, 4, 6, 11, 12, 22, 23, 33, 44, 46, 66, 69, 92, 132, 138, 253, 276, 506, 759, 1012, 1518 and 3036
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.