22 × 3 × 13 × 17
1, 2, 3, 4, 6, 12, 13, 17, 26, 34, 39, 51, 52, 68, 78, 102, 156, 204, 221, 442, 663, 884, 1326 and 2652
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.