2 × 32 × 7 × 17
1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071 and 2142
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.