22 × 3 × 13 × 23
1, 2, 3, 4, 6, 12, 13, 23, 26, 39, 46, 52, 69, 78, 92, 138, 156, 276, 299, 598, 897, 1196, 1794 and 3588
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.