22 × 3 × 7 × 29
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 29, 42, 58, 84, 87, 116, 174, 203, 348, 406, 609, 812, 1218 and 2436
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.